Default Branch Search is Too Slow

[aj-codecov]

Describe the bug
Default Branch search is so slow that it sometimes doesn't resolve for larger repos.

To Reproduce
Org > Repo > Configuration > General > default branch dropdown > search for something > it's slow
Expected behavior
It's at least fast enough that when searching for a branch name in a large repo like Sentry's that we actually surface a result instead of an infini-spinner.

Screenshots

[eliatcodecov]

It's unclear to me where precisely this problem is: front end, API , database. My guess is to probably hand this to someone to investigate from the API/database perspective to see if this search call can work better. It could also be benefitted potentially from a debounce on the front end if that's not already in place.