Move consumers off bsearch endpoint

[lukasolson]

Summary

Part of #186139.

Moves direct consumers off of the internal/bsearch endpoint and onto the internal/search.

This is in preparation for removing the internal/bsearch endpoint entirely.

Updates automated tests to mock/use the correct service moving forward.

Checklist

• Documentation was added for features that require explanation or tutorials
• Unit or functional tests were updated or added to match the most common scenarios
• Flaky Test Runner was used on any tests changed

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cc @lukasolson