Faster joins: persist to database (#12012)

When we get a partial_state response from send_join, store information in the
database about it:
 * store a record about the room as a whole having partial state, and stash the
   list of member servers too.
 * flag the join event itself as having partial state
 * also, for any new events whose prev-events are partial-stated, note that
   they will *also* be partial-stated.

We don't yet make any attempt to interpret this data, so API calls (and a bunch
of other things) are just going to get incorrect data.

synapse/storage/databases/main/events_worker.py

@@ -1953,3 +1953,31 @@ class EventsWorkerStore(SQLBaseStore):
             "get_event_id_for_timestamp_txn",
             get_event_id_for_timestamp_txn,
         )
+
+    @cachedList("is_partial_state_event", list_name="event_ids")
+    async def get_partial_state_events(
+        self, event_ids: Collection[str]
+    ) -> Dict[str, bool]:
+        """Checks which of the given events have partial state"""
+        result = await self.db_pool.simple_select_many_batch(
+            table="partial_state_events",
+            column="event_id",
+            iterable=event_ids,
+            retcols=["event_id"],
+            desc="get_partial_state_events",
+        )
+        # convert the result to a dict, to make @cachedList work
+        partial = {r["event_id"] for r in result}
+        return {e_id: e_id in partial for e_id in event_ids}
+
+    @cached()
+    async def is_partial_state_event(self, event_id: str) -> bool:
+        """Checks if the given event has partial state"""
+        result = await self.db_pool.simple_select_one_onecol(
+            table="partial_state_events",
+            keyvalues={"event_id": event_id},
+            retcol="1",
+            allow_none=True,
+            desc="is_partial_state_event",
+        )
+        return result is not None