Investigate optimizations for the searchGroups endpoint

The query for the endpoint has multiple joins, and there could be ways to optimize the query performance. One possible change could involve updating the database schema.

To test database performance, integration tests in the src/test/java folder can be run.

Open a PR or comment on this issue if you have recommendations for an optimization.

Start by locating the searchGroups endpoint and its multi-join query in the Java backend. Run the integration tests under src/test/java to establish database-performance results, then investigate the query and any relevant schema options. Done means documenting a supported optimization or opening a PR with measured performance evidence.

Written by the indexing model from the issue text.