Add basic organization switcher

See merge request https://gitlab.com/gitlab-org/gitlab/-/merge_requests/140603



Merged-by: Coung Ngo <cngo@gitlab.com>
Approved-by: Emily Bauman <ebauman@gitlab.com>
Approved-by: Ammar Alakkad <aalakkad@gitlab.com>
Approved-by: Coung Ngo <cngo@gitlab.com>
Co-authored-by: Peter Hegman <phegman@gitlab.com>