This is the sub-ticket focusing on test coverage parity with $search for sharding. A collection of tests to consider:

https://github.com/10gen/mongo-enterprise-modules/commit/c3336710dbf19fa61db3bc6dd7f004af66e6922d

Note that

1. These tests were copied directly from jstests/search
   1. The tests from focusing on the features we don't support in $vectorSearch are excluded. For example,  $SearchMeta, stored source, limit pushdown, etc.
   2. There might be a few tests that can still be further excluded.
2. We need to modify these tests to work for vector search. For example:
   1. Replace $search with $vectorSearch
   2. Change to mongot KNN command
   3. Remove the mocks for planShardedSearch