diff --git a/ee/spec/elastic/migrate/20230307102400_backfill_hashed_root_namespace_id_on_notes_spec.rb b/ee/spec/elastic/migrate/20230307102400_backfill_hashed_root_namespace_id_on_notes_spec.rb
index e3d9261c632d93dd8d7c19c7eb94d2790fdaac5c..83aad964f0013e6ca9f6daead0ff6cbf93088dae 100644
--- a/ee/spec/elastic/migrate/20230307102400_backfill_hashed_root_namespace_id_on_notes_spec.rb
+++ b/ee/spec/elastic/migrate/20230307102400_backfill_hashed_root_namespace_id_on_notes_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230307102400_backfill_hashed_root_namespace_id_on_notes.rb')
 
-RSpec.describe BackfillHashedRootNamespaceIdOnNotes, :elastic_delete_by_query, feature_category: :global_search do
+RSpec.describe BackfillHashedRootNamespaceIdOnNotes, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230307102400
 end
diff --git a/ee/spec/elastic/migrate/20230316150000_add_hashed_root_namespace_id_to_merge_requests_spec.rb b/ee/spec/elastic/migrate/20230316150000_add_hashed_root_namespace_id_to_merge_requests_spec.rb
index c479e82418e60c77fd6f6e022714f9ef33e66857..9daf299164fc9e94417b651e37960b3b02dfe89e 100644
--- a/ee/spec/elastic/migrate/20230316150000_add_hashed_root_namespace_id_to_merge_requests_spec.rb
+++ b/ee/spec/elastic/migrate/20230316150000_add_hashed_root_namespace_id_to_merge_requests_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230316150000_add_hashed_root_namespace_id_to_merge_requests.rb')
 
-RSpec.describe AddHashedRootNamespaceIdToMergeRequests, :elastic_delete_by_query, feature_category: :global_search do
+RSpec.describe AddHashedRootNamespaceIdToMergeRequests, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230316150000
 end
diff --git a/ee/spec/elastic/migrate/20230317120500_add_hashed_root_namespace_id_to_issues_spec.rb b/ee/spec/elastic/migrate/20230317120500_add_hashed_root_namespace_id_to_issues_spec.rb
index d3bdda3a9a9ad5647a9767f38595cfee06bf2f10..e807443c3df428c659fada3b70eb2ef10f736b2b 100644
--- a/ee/spec/elastic/migrate/20230317120500_add_hashed_root_namespace_id_to_issues_spec.rb
+++ b/ee/spec/elastic/migrate/20230317120500_add_hashed_root_namespace_id_to_issues_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230317120500_add_hashed_root_namespace_id_to_issues.rb')
 
-RSpec.describe AddHashedRootNamespaceIdToIssues, :elastic, :sidekiq_inline, feature_category: :global_search do
+RSpec.describe AddHashedRootNamespaceIdToIssues, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230317120500
 end
diff --git a/ee/spec/elastic/migrate/20230320011400_add_hashed_root_namespace_id_to_commits_spec.rb b/ee/spec/elastic/migrate/20230320011400_add_hashed_root_namespace_id_to_commits_spec.rb
index b2f891d9f3368abc3d5c0cff52760f20fed85f17..54c4b44605f6ae997904bd84a1ed9d8d5ec7dcaf 100644
--- a/ee/spec/elastic/migrate/20230320011400_add_hashed_root_namespace_id_to_commits_spec.rb
+++ b/ee/spec/elastic/migrate/20230320011400_add_hashed_root_namespace_id_to_commits_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230320011400_add_hashed_root_namespace_id_to_commits.rb')
 
-RSpec.describe AddHashedRootNamespaceIdToCommits, :elastic, :sidekiq_inline, feature_category: :global_search do
+RSpec.describe AddHashedRootNamespaceIdToCommits, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230320011400
 end
diff --git a/ee/spec/elastic/migrate/20230321091100_backfill_hashed_root_namespace_id_on_issues_spec.rb b/ee/spec/elastic/migrate/20230321091100_backfill_hashed_root_namespace_id_on_issues_spec.rb
index bf585ff1d3c7f281358b349cd432bdbe83aa75f7..671389eab57f45eafee434a3909d79b975981921 100644
--- a/ee/spec/elastic/migrate/20230321091100_backfill_hashed_root_namespace_id_on_issues_spec.rb
+++ b/ee/spec/elastic/migrate/20230321091100_backfill_hashed_root_namespace_id_on_issues_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230321091100_backfill_hashed_root_namespace_id_on_issues.rb')
 
-RSpec.describe BackfillHashedRootNamespaceIdOnIssues, :elastic_delete_by_query, feature_category: :global_search do
+RSpec.describe BackfillHashedRootNamespaceIdOnIssues, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230321091100
 end
diff --git a/ee/spec/elastic/migrate/20230321202400_backfill_hashed_root_namespace_id_on_merge_requests_spec.rb b/ee/spec/elastic/migrate/20230321202400_backfill_hashed_root_namespace_id_on_merge_requests_spec.rb
index 13be6760e852ee1919cbb36201fb27983f419d10..b710c9283065b102ef8b317d3c4386e1bc08c007 100644
--- a/ee/spec/elastic/migrate/20230321202400_backfill_hashed_root_namespace_id_on_merge_requests_spec.rb
+++ b/ee/spec/elastic/migrate/20230321202400_backfill_hashed_root_namespace_id_on_merge_requests_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230321202400_backfill_hashed_root_namespace_id_on_merge_requests.rb')
 
-RSpec.describe BackfillHashedRootNamespaceIdOnMergeRequests, :elastic_delete_by_query, feature_category: :global_search do
+RSpec.describe BackfillHashedRootNamespaceIdOnMergeRequests, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230321202400
 end
diff --git a/ee/spec/elastic/migrate/20230405500000_backfill_wiki_permissions_in_main_index_spec.rb b/ee/spec/elastic/migrate/20230405500000_backfill_wiki_permissions_in_main_index_spec.rb
index 8bcd3873df317c798f0c1771cbb15531c3018eb3..ff82bf9a2dfb930563945e0ce58ec9deb943159d 100644
--- a/ee/spec/elastic/migrate/20230405500000_backfill_wiki_permissions_in_main_index_spec.rb
+++ b/ee/spec/elastic/migrate/20230405500000_backfill_wiki_permissions_in_main_index_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230405500000_backfill_wiki_permissions_in_main_index.rb')
 
-RSpec.describe BackfillWikiPermissionsInMainIndex, :elastic_delete_by_query, :sidekiq_inline, feature_category: :global_search do
+RSpec.describe BackfillWikiPermissionsInMainIndex, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230405500000
 end
diff --git a/ee/spec/elastic/migrate/20230427555555_backfill_hidden_on_merge_requests_spec.rb b/ee/spec/elastic/migrate/20230427555555_backfill_hidden_on_merge_requests_spec.rb
index c509e582907a7a11d056f6bc2e4292474134772d..589cf409db61eb68090bfec8c709bac751dd272f 100644
--- a/ee/spec/elastic/migrate/20230427555555_backfill_hidden_on_merge_requests_spec.rb
+++ b/ee/spec/elastic/migrate/20230427555555_backfill_hidden_on_merge_requests_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230427555555_backfill_hidden_on_merge_requests.rb')
 
-RSpec.describe BackfillHiddenOnMergeRequests, :elastic_delete_by_query, feature_category: :global_search do
+RSpec.describe BackfillHiddenOnMergeRequests, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230427555555
 end
diff --git a/ee/spec/elastic/migrate/20230428500000_add_suffix_project_in_wiki_rid_spec.rb b/ee/spec/elastic/migrate/20230428500000_add_suffix_project_in_wiki_rid_spec.rb
index 66bdd747e828b10cde4d8adb111ea017efbb9bf1..4114b4922f8e3f0557f1eb02bcb9c44a09593bb6 100644
--- a/ee/spec/elastic/migrate/20230428500000_add_suffix_project_in_wiki_rid_spec.rb
+++ b/ee/spec/elastic/migrate/20230428500000_add_suffix_project_in_wiki_rid_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230428500000_add_suffix_project_in_wiki_rid.rb')
 
-RSpec.describe AddSuffixProjectInWikiRid, :elastic_clean, :sidekiq_inline, feature_category: :global_search do
+RSpec.describe AddSuffixProjectInWikiRid, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230428500000
 end
diff --git a/ee/spec/elastic/migrate/20230607500000_backfill_milestone_permissions_to_milestone_documents_spec.rb b/ee/spec/elastic/migrate/20230607500000_backfill_milestone_permissions_to_milestone_documents_spec.rb
index 2e19a5560e64810134a4c58ec2e93ecbf0b971de..c54c272ddeb0df6c6cec95d7ac05d840b3674a79 100644
--- a/ee/spec/elastic/migrate/20230607500000_backfill_milestone_permissions_to_milestone_documents_spec.rb
+++ b/ee/spec/elastic/migrate/20230607500000_backfill_milestone_permissions_to_milestone_documents_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230607500000_backfill_milestone_permissions_to_milestone_documents.rb')
 
-RSpec.describe BackfillMilestonePermissionsToMilestoneDocuments, :elastic_delete_by_query, feature_category: :global_search do
+RSpec.describe BackfillMilestonePermissionsToMilestoneDocuments, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230607500000
 end
diff --git a/ee/spec/elastic/migrate/20230613555555_add_schema_version_to_commits_spec.rb b/ee/spec/elastic/migrate/20230613555555_add_schema_version_to_commits_spec.rb
index 64d4636c7495766b1b0f1ea4653022ddd2da983a..52d534f903f6e510cc648173792b24ce8d14b8de 100644
--- a/ee/spec/elastic/migrate/20230613555555_add_schema_version_to_commits_spec.rb
+++ b/ee/spec/elastic/migrate/20230613555555_add_schema_version_to_commits_spec.rb
@@ -3,6 +3,6 @@
 require 'spec_helper'
 require File.expand_path('ee/elastic/migrate/20230613555555_add_schema_version_to_commits.rb')
 
-RSpec.describe AddSchemaVersionToCommits, :elastic, :sidekiq_inline, feature_category: :global_search do
+RSpec.describe AddSchemaVersionToCommits, feature_category: :global_search do
   it_behaves_like 'a deprecated Advanced Search migration', 20230613555555
 end
diff --git a/keeps/mark_old_advanced_search_migrations_as_obsolete.rb b/keeps/mark_old_advanced_search_migrations_as_obsolete.rb
index 2b0e8100c09fec1616ec9f50b8ae98b89202b32a..b4a8428eed14312ad1cf0c661818a5e5bbb9cf2d 100644
--- a/keeps/mark_old_advanced_search_migrations_as_obsolete.rb
+++ b/keeps/mark_old_advanced_search_migrations_as_obsolete.rb
@@ -131,7 +131,7 @@ def create_mark_obsolete_change(version, migration_data)
       change.changed_files << migration_data[:file]
 
       if File.exist?(migration_data[:spec_file])
-        add_obsolete_to_migration_spec(version, migration_data[:spec_file])
+        add_obsolete_to_migration_spec(version, migration_data[:spec_file], migration_data[:yaml_content]['name'])
         change.changed_files << migration_data[:spec_file]
       end
 
@@ -154,12 +154,15 @@ def add_obsolete_to_migration(file)
       File.open(file, 'a') { |f| f.write("\n#{klass_name}.prepend ::Elastic::MigrationObsolete\n") }
     end
 
-    def add_obsolete_to_migration_spec(version, file)
+    def add_obsolete_to_migration_spec(version, file, name)
+      describe = "RSpec.describe #{name}, feature_category: :global_search"
       content = "it_behaves_like 'a deprecated Advanced Search migration', #{version}"
 
       source = RuboCop::ProcessedSource.new(File.read(file), RuboCop::ConfigStore.new.for_file('.').target_ruby_version)
       rewriter = Parser::Source::TreeRewriter.new(source.buffer)
+      describe_line = source.ast.each_node(:block).first.each_node(:send).first
       describe_block = source.ast.each_node(:block).first.each_node(:begin).first
+      rewriter.replace(describe_line.loc.expression, describe)
       rewriter.replace(describe_block.loc.expression, content)
       process = rewriter.process.lstrip.gsub(/\n{3,}/, "\n\n")