Searching and filtering members in a group

Note that we use pagination, but want to search / filter for every member. Also keep in mind performance with large number of memberships.

Start by tracing the group membership listing entry point and its pagination behavior. Determine how searching and filtering should cover every member without loading an impractically large membership set, then verify the result with the relevant existing request or model tests; no specific files or tests are named in the issue.

Written by the indexing model from the issue text.