Revert the general exception recording introduced in #13814 (#13969)

* Maybe not catch all errors to avoid things in the nature-of CancelledError

See #13815 (comment)

* Remove general exception tracking

* Add changelog

changelog.d/13969.misc

@@ -0,0 +1 @@
+Revert catch-all exceptions being recorded as event pull attempt failures (only handle what we know about).

synapse/handlers/federation_event.py

@@ -866,11 +866,6 @@ 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:
@@ -913,11 +908,6 @@ 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(