Merge branch 'leipert-fix-search-sidebar-in-vite' into 'master'

Improve logic around the header in the search nav

See merge request https://gitlab.com/gitlab-org/gitlab/-/merge_requests/148169



Merged-by: Mark Florian <mflorian@gitlab.com>
Approved-by: Terri Chu <tchu@gitlab.com>
Approved-by: Tomas Bulva <tbulva@gitlab.com>
Approved-by: Aboobacker MK <akarakath@gitlab.com>
Approved-by: Mark Florian <mflorian@gitlab.com>
Reviewed-by: Terri Chu <tchu@gitlab.com>
Reviewed-by: Tomas Bulva <tbulva@gitlab.com>
Co-authored-by: Lukas Eipert <leipert@gitlab.com>