Fixups to new push stream (#17038)

Follow on from #17037

docker/configure_workers_and_start.py

@@ -310,6 +310,13 @@ WORKERS_CONFIG: Dict[str, Dict[str, Any]] = {
         "shared_extra_conf": {},
         "worker_extra_conf": "",
     },
+    "push_rules": {
+        "app": "synapse.app.generic_worker",
+        "listener_resources": ["client", "replication"],
+        "endpoint_patterns": ["^/_matrix/client/(api/v1|r0|v3|unstable)/pushrules/"],
+        "shared_extra_conf": {},
+        "worker_extra_conf": "",
+    },
 }
 
 # Templates for sections that may be inserted multiple times in config files
@@ -401,6 +408,7 @@ def add_worker_roles_to_shared_config(
         "receipts",
         "to_device",
         "typing",
+        "push_rules",
     ]
 
     # Worker-type specific sharding config. Now a single worker can fulfill multiple