Record any exception when processing a pulled event (#13814)

Part of #13700 and #13356

Follow-up to #13589

changelog.d/13589.feature

@@ -1 +1 @@
-Keep track when we attempt to backfill an event but fail so we can intelligently back-off in the future.
+Keep track when we fail to process a pulled event over federation so we can intelligently back-off in the future.

changelog.d/13814.feature

@@ -0,0 +1 @@
+Keep track when we fail to process a pulled event over federation so we can intelligently back-off in the future.

synapse/handlers/federation_event.py

@@ -866,6 +866,11 @@ async def _process_pulled_event(
                 event.room_id, event_id, str(err)
             )
             return
+        except Exception as exc:
+            await self._store.record_event_failed_pull_attempt(
+                event.room_id, event_id, str(exc)
+            )
+            raise exc
 
         try:
             try:
@@ -908,6 +913,11 @@ async def _process_pulled_event(
                 logger.warning("Pulled event %s failed history check.", event_id)
             else:
                 raise
+        except Exception as exc:
+            await self._store.record_event_failed_pull_attempt(
+                event.room_id, event_id, str(exc)
+            )
+            raise exc
 
     @trace
     async def _compute_event_context_with_maybe_missing_prevs(