Fix a cache-invalidation bug for worker-based deployments (#5920)

Some of the caches on worker processes were not being correctly invalidated
when a room's state was changed in a way that did not affect the membership
list of the room.

We need to make sure we send out cache invalidations even when no memberships
are changing.

changelog.d/5920.bugfix

@@ -0,0 +1 @@
+Fix a cache-invalidation bug for worker-based deployments.

synapse/storage/_base.py

@@ -1395,14 +1395,22 @@ def _invalidate_state_caches_and_stream(self, txn, room_id, members_changed):
         """
         txn.call_after(self._invalidate_state_caches, room_id, members_changed)
 
-        # We need to be careful that the size of the `members_changed` list
-        # isn't so large that it causes problems sending over replication, so we
-        # send them in chunks.
-        # Max line length is 16K, and max user ID length is 255, so 50 should
-        # be safe.
-        for chunk in batch_iter(members_changed, 50):
-            keys = itertools.chain([room_id], chunk)
-            self._send_invalidation_to_replication(txn, _CURRENT_STATE_CACHE_NAME, keys)
+        if members_changed:
+            # We need to be careful that the size of the `members_changed` list
+            # isn't so large that it causes problems sending over replication, so we
+            # send them in chunks.
+            # Max line length is 16K, and max user ID length is 255, so 50 should
+            # be safe.
+            for chunk in batch_iter(members_changed, 50):
+                keys = itertools.chain([room_id], chunk)
+                self._send_invalidation_to_replication(
+                    txn, _CURRENT_STATE_CACHE_NAME, keys
+                )
+        else:
+            # if no members changed, we still need to invalidate the other caches.
+            self._send_invalidation_to_replication(
+                txn, _CURRENT_STATE_CACHE_NAME, [room_id]
+            )
 
     def _invalidate_state_caches(self, room_id, members_changed):
         """Invalidates caches that are based on the current state, but does