Stop getting missing prev_events after we already know their signature is invalid (#13816)

While https://github.com/matrix-org/synapse/pull/13635 stops us from doing the slow thing after we've already done it once, this PR stops us from doing one of the slow things in the first place.

Related to
 - https://github.com/matrix-org/synapse/issues/13622
    - https://github.com/matrix-org/synapse/pull/13635
 - https://github.com/matrix-org/synapse/issues/13676

Part of https://github.com/matrix-org/synapse/issues/13356

Follow-up to https://github.com/matrix-org/synapse/pull/13815 which tracks event signature failures.

With this PR, we avoid the call to the costly `_get_state_ids_after_missing_prev_event` because the signature failure will count as an attempt before and we filter events based on the backoff before calling `_get_state_ids_after_missing_prev_event` now.

For example, this will save us 156s out of the 185s total that this `matrix.org` `/messages` request. If you want to see the full Jaeger trace of this, you can drag and drop this `trace.json` into your own Jaeger, https://gist.github.com/MadLittleMods/4b12d0d0afe88c2f65ffcc907306b761

To explain this exact scenario around `/messages` -> backfill, we call `/backfill` and first check the signatures of the 100 events. We see bad signature for `$luA4l7QHhf_jadH3mI-AyFqho0U2Q-IXXUbGSMq6h6M` and `$zuOn2Rd2vsC7SUia3Hp3r6JSkSFKcc5j3QTTqW_0jDw` (both member events). Then we process the 98 events remaining that have valid signatures but one of the events references `$luA4l7QHhf_jadH3mI-AyFqho0U2Q-IXXUbGSMq6h6M` as a `prev_event`. So we have to do the whole `_get_state_ids_after_missing_prev_event` rigmarole which pulls in those same events which fail again because the signatures are still invalid.

 - `backfill`
    - `outgoing-federation-request` `/backfill`
    - `_check_sigs_and_hash_and_fetch`
       - `_check_sigs_and_hash_and_fetch_one` for each event received over backfill
          - ❗ `$luA4l7QHhf_jadH3mI-AyFqho0U2Q-IXXUbGSMq6h6M` fails with `Signature on retrieved event was invalid.`: `unable to verify signature for sender domain xxx: 401: Failed to find any key to satisfy: _FetchKeyRequest(...)`
          - ❗ `$zuOn2Rd2vsC7SUia3Hp3r6JSkSFKcc5j3QTTqW_0jDw` fails with `Signature on retrieved event was invalid.`: `unable to verify signature for sender domain xxx: 401: Failed to find any key to satisfy: _FetchKeyRequest(...)`
   - `_process_pulled_events`
      - `_process_pulled_event` for each validated event
         - ❗ Event `$Q0iMdqtz3IJYfZQU2Xk2WjB5NDF8Gg8cFSYYyKQgKJ0` references `$luA4l7QHhf_jadH3mI-AyFqho0U2Q-IXXUbGSMq6h6M` as a `prev_event` which is missing so we try to get it
            - `_get_state_ids_after_missing_prev_event`
               - `outgoing-federation-request` `/state_ids`
               - ❗ `get_pdu` for `$luA4l7QHhf_jadH3mI-AyFqho0U2Q-IXXUbGSMq6h6M` which fails the signature check again
               - ❗ `get_pdu` for `$zuOn2Rd2vsC7SUia3Hp3r6JSkSFKcc5j3QTTqW_0jDw` which fails the signature check

synapse/storage/databases/main/event_federation.py

@@ -1501,6 +1501,12 @@ class EventFederationWorkerStore(SignatureWorkerStore, EventsWorkerStore, SQLBas
             event_id: The event that failed to be fetched or processed
             cause: The error message or reason that we failed to pull the event
         """
+        logger.debug(
+            "record_event_failed_pull_attempt room_id=%s, event_id=%s, cause=%s",
+            room_id,
+            event_id,
+            cause,
+        )
         await self.db_pool.runInteraction(
             "record_event_failed_pull_attempt",
             self._record_event_failed_pull_attempt_upsert_txn,
@@ -1530,6 +1536,54 @@ class EventFederationWorkerStore(SignatureWorkerStore, EventsWorkerStore, SQLBas
 
         txn.execute(sql, (room_id, event_id, 1, self._clock.time_msec(), cause))
 
+    @trace
+    async def get_event_ids_to_not_pull_from_backoff(
+        self,
+        room_id: str,
+        event_ids: Collection[str],
+    ) -> List[str]:
+        """
+        Filter down the events to ones that we've failed to pull before recently. Uses
+        exponential backoff.
+
+        Args:
+            room_id: The room that the events belong to
+            event_ids: A list of events to filter down
+
+        Returns:
+            List of event_ids that should not be attempted to be pulled
+        """
+        event_failed_pull_attempts = await self.db_pool.simple_select_many_batch(
+            table="event_failed_pull_attempts",
+            column="event_id",
+            iterable=event_ids,
+            keyvalues={},
+            retcols=(
+                "event_id",
+                "last_attempt_ts",
+                "num_attempts",
+            ),
+            desc="get_event_ids_to_not_pull_from_backoff",
+        )
+
+        current_time = self._clock.time_msec()
+        return [
+            event_failed_pull_attempt["event_id"]
+            for event_failed_pull_attempt in event_failed_pull_attempts
+            # Exponential back-off (up to the upper bound) so we don't try to
+            # pull the same event over and over. ex. 2hr, 4hr, 8hr, 16hr, etc.
+            if current_time
+            < event_failed_pull_attempt["last_attempt_ts"]
+            + (
+                2
+                ** min(
+                    event_failed_pull_attempt["num_attempts"],
+                    BACKFILL_EVENT_EXPONENTIAL_BACKOFF_MAXIMUM_DOUBLING_STEPS,
+                )
+            )
+            * BACKFILL_EVENT_EXPONENTIAL_BACKOFF_STEP_MILLISECONDS
+        ]
+
     async def get_missing_events(
         self,
         room_id: str,