Automatic merge from submit-queue (batch tested with PRs 60106, 59510, 60263, 60063, 59088). If you want to cherry-pick this change to another branch, please follow the instructions <a href="https://github.com/kubernetes/community/blob/master/contributors/devel/cherry-picks.md">here</a>.

Refactor service storage to remove registry wrapper

This exposes the correct table exporter to the API endpoint, which is a prereq for server side GET to beta. Removing the use of the registry simplifies a few complex changes but results in test abstractions changing.

Part of #58536