Fix the auth provider on the logins metric (#9573)

We either need to pass the auth provider over the replication api, or make sure
we report the auth provider on the worker that received the request. I've gone
with the latter.

synapse/handlers/register.py

@@ -16,7 +16,7 @@
 """Contains functions for registering clients."""
 
 import logging
-from typing import TYPE_CHECKING, Iterable, List, Optional, Tuple
+from typing import TYPE_CHECKING, Dict, Iterable, List, Optional, Tuple
 
 from prometheus_client import Counter
 
@@ -82,6 +82,7 @@ class RegistrationHandler(BaseHandler):
             )
         else:
             self.device_handler = hs.get_device_handler()
+            self._register_device_client = self.register_device_inner
             self.pusher_pool = hs.get_pusherpool()
 
         self.session_lifetime = hs.config.session_lifetime
@@ -678,17 +679,35 @@ class RegistrationHandler(BaseHandler):
         Returns:
             Tuple of device ID and access token
         """
+        res = await self._register_device_client(
+            user_id=user_id,
+            device_id=device_id,
+            initial_display_name=initial_display_name,
+            is_guest=is_guest,
+            is_appservice_ghost=is_appservice_ghost,
+        )
 
-        if self.hs.config.worker_app:
-            r = await self._register_device_client(
-                user_id=user_id,
-                device_id=device_id,
-                initial_display_name=initial_display_name,
-                is_guest=is_guest,
-                is_appservice_ghost=is_appservice_ghost,
-            )
-            return r["device_id"], r["access_token"]
+        login_counter.labels(
+            guest=is_guest,
+            auth_provider=(auth_provider_id or ""),
+        ).inc()
 
+        return res["device_id"], res["access_token"]
+
+    async def register_device_inner(
+        self,
+        user_id: str,
+        device_id: Optional[str],
+        initial_display_name: Optional[str],
+        is_guest: bool = False,
+        is_appservice_ghost: bool = False,
+    ) -> Dict[str, str]:
+        """Helper for register_device
+
+        Does the bits that need doing on the main process. Not for use outside this
+        class and RegisterDeviceReplicationServlet.
+        """
+        assert not self.hs.config.worker_app
         valid_until_ms = None
         if self.session_lifetime is not None:
             if is_guest:
@@ -713,12 +732,7 @@ class RegistrationHandler(BaseHandler):
                 is_appservice_ghost=is_appservice_ghost,
             )
 
-        login_counter.labels(
-            guest=is_guest,
-            auth_provider=(auth_provider_id or ""),
-        ).inc()
-
-        return (registered_device_id, access_token)
+        return {"device_id": registered_device_id, "access_token": access_token}
 
     async def post_registration_actions(
         self, user_id: str, auth_result: dict, access_token: Optional[str]