Type the connection store against the config subset it uses

The store only needs user/requester/conn_id from the sync config, and is
shared between sliding sync and paginated sync (MSC4525), so type its
methods with a Protocol both configs satisfy instead of SlidingSyncConfig
(fixes the mypy failure on PaginatedSyncConfig at the
get_and_clear_connection_positions call site, and drops the now-redundant
ignore on record_new_state).

synapse/handlers/sliding_sync/paginated.py

@@ -397,7 +397,7 @@ class PaginatedSyncHandler(SlidingSyncHandler):
         new_connection_state.rooms.record_sent_rooms(relevant_rooms_to_send_map.keys())
 
         connection_position = await self.connection_store.record_new_state(
-            sync_config=sync_config,  # type: ignore[arg-type]
+            sync_config=sync_config,
             from_token=from_token,
             new_connection_state=new_connection_state,
         )

synapse/handlers/sliding_sync/store.py

@@ -13,22 +13,38 @@
 #
 
 import logging
+from typing import Protocol
 
 import attr
 
 from synapse.logging.opentracing import trace
 from synapse.storage.databases.main import DataStore
-from synapse.types import SlidingSyncStreamToken
+from synapse.types import Requester, SlidingSyncStreamToken, UserID
 from synapse.types.handlers.sliding_sync import (
     MutablePerConnectionState,
     PerConnectionState,
-    SlidingSyncConfig,
 )
 from synapse.util.clock import Clock
 
 logger = logging.getLogger(__name__)
 
 
+class SlidingSyncConnectionConfig(Protocol):
+    """The subset of a sync config the connection store needs: who the
+    connection belongs to and its client-chosen ID. Satisfied by both
+    `SlidingSyncConfig` and `PaginatedSyncConfig` (MSC4525), which share the
+    per-connection room-tracking machinery."""
+
+    @property
+    def user(self) -> UserID: ...
+
+    @property
+    def requester(self) -> Requester: ...
+
+    @property
+    def conn_id(self) -> str | None: ...
+
+
 @attr.s(auto_attribs=True)
 class SlidingSyncConnectionStore:
     """In-memory store of per-connection state, including what rooms we have
@@ -63,7 +79,7 @@ class SlidingSyncConnectionStore:
 
     async def get_and_clear_connection_positions(
         self,
-        sync_config: SlidingSyncConfig,
+        sync_config: SlidingSyncConnectionConfig,
         from_token: SlidingSyncStreamToken | None,
     ) -> PerConnectionState:
         """Fetch the per-connection state for the token.
@@ -90,7 +106,7 @@ class SlidingSyncConnectionStore:
     @trace
     async def record_new_state(
         self,
-        sync_config: SlidingSyncConfig,
+        sync_config: SlidingSyncConnectionConfig,
         from_token: SlidingSyncStreamToken | None,
         new_connection_state: MutablePerConnectionState,
     ) -> int: