Removed `request_key` from the `SyncConfig` (moved outside as its own function parameter) so it doesn't have to flow into `_generate_sync_entry_for_xxx` methods. This way we can separate the concerns of caching from generating the response and reuse the `_generate_sync_entry_for_xxx` functions as we see fit. Plus caching doesn't really have anything to do with the config of sync.
Split from https://github.com/element-hq/synapse/pull/17167
Spawning from https://github.com/element-hq/synapse/pull/17167#discussion_r1601497279
