git: Bump minimum version to v2.37.0

This has been the default version for a while on production (behind a feature flag). We also recently deleted the feature flag. Now let's bump the minimum version to v2.37.0. This is required since one of the features (adding --batch-command support to git-cat-file(1)) requires git >v2.36.0.

Bunch of other commits to cleanup v2.35.0 related code.

Part of #4192 (closed) Depends on !4874 (merged)

Note: Should be merged in one release after !4874 (merged)