Server-side search of unsynced messages—especially in rooms/conversations marked as archived

[HammyHavoc]

During the discussion at #2189 (comment), it occurred to me that supporting server-side search for messages that haven't yet been synced to the client could offer significant benefits. This would be particularly useful in rooms with the proposed archived status, where syncing full message history to every client isn't ideal or necessary.

By handling the search query server-side and returning only the relevant results to the user, it could greatly reduce both server and client resource usage and bandwidth, especially for older or infrequently accessed conversations. This would also improve the experience for users accessing large or archived rooms without the overhead of syncing large histories to their device.