diff --git a/changelog.d/18509.bugfix b/changelog.d/18509.bugfix
new file mode 100644
index 0000000000..2c821d0395
--- /dev/null
+++ b/changelog.d/18509.bugfix
@@ -0,0 +1 @@
+Fix `KeyError` on background updates when using split main/state databases.
diff --git a/rust/src/identifier.rs b/rust/src/identifier.rs
index b70f6a30c7..03d1ebdc8a 100644
--- a/rust/src/identifier.rs
+++ b/rust/src/identifier.rs
@@ -27,7 +27,7 @@ pub enum IdentifierError {
 
 impl fmt::Display for IdentifierError {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        write!(f, "{:?}", self)
+        write!(f, "{self:?}")
     }
 }
 
diff --git a/synapse/storage/databases/main/events_bg_updates.py b/synapse/storage/databases/main/events_bg_updates.py
index 5c83a9f779..8a59091da0 100644
--- a/synapse/storage/databases/main/events_bg_updates.py
+++ b/synapse/storage/databases/main/events_bg_updates.py
@@ -294,6 +294,27 @@ class EventsBackgroundUpdatesStore(StreamWorkerStore, StateDeltasStore, SQLBaseS
             where_clause="NOT outlier",
         )
 
+        # These indices are needed to validate the foreign key constraint
+        # when events are deleted.
+        self.db_pool.updates.register_background_index_update(
+            _BackgroundUpdates.CURRENT_STATE_EVENTS_STREAM_ORDERING_INDEX_UPDATE_NAME,
+            index_name="current_state_events_stream_ordering_idx",
+            table="current_state_events",
+            columns=["event_stream_ordering"],
+        )
+        self.db_pool.updates.register_background_index_update(
+            _BackgroundUpdates.ROOM_MEMBERSHIPS_STREAM_ORDERING_INDEX_UPDATE_NAME,
+            index_name="room_memberships_stream_ordering_idx",
+            table="room_memberships",
+            columns=["event_stream_ordering"],
+        )
+        self.db_pool.updates.register_background_index_update(
+            _BackgroundUpdates.LOCAL_CURRENT_MEMBERSHIP_STREAM_ORDERING_INDEX_UPDATE_NAME,
+            index_name="local_current_membership_stream_ordering_idx",
+            table="local_current_membership",
+            columns=["event_stream_ordering"],
+        )
+
         # Handle background updates for Sliding Sync tables
         #
         self.db_pool.updates.register_background_update_handler(
diff --git a/synapse/storage/databases/state/bg_updates.py b/synapse/storage/databases/state/bg_updates.py
index 5b594fe8dd..ac38b2ab19 100644
--- a/synapse/storage/databases/state/bg_updates.py
+++ b/synapse/storage/databases/state/bg_updates.py
@@ -290,16 +290,6 @@ class StateBackgroundUpdateStore(StateGroupBackgroundUpdateStore):
     STATE_GROUPS_ROOM_INDEX_UPDATE_NAME = "state_groups_room_id_idx"
     STATE_GROUP_EDGES_UNIQUE_INDEX_UPDATE_NAME = "state_group_edges_unique_idx"
 
-    CURRENT_STATE_EVENTS_STREAM_ORDERING_INDEX_UPDATE_NAME = (
-        "current_state_events_stream_ordering_idx"
-    )
-    ROOM_MEMBERSHIPS_STREAM_ORDERING_INDEX_UPDATE_NAME = (
-        "room_memberships_stream_ordering_idx"
-    )
-    LOCAL_CURRENT_MEMBERSHIP_STREAM_ORDERING_INDEX_UPDATE_NAME = (
-        "local_current_membership_stream_ordering_idx"
-    )
-
     def __init__(
         self,
         database: DatabasePool,
@@ -336,27 +326,6 @@ class StateBackgroundUpdateStore(StateGroupBackgroundUpdateStore):
             replaces_index="state_group_edges_idx",
         )
 
-        # These indices are needed to validate the foreign key constraint
-        # when events are deleted.
-        self.db_pool.updates.register_background_index_update(
-            self.CURRENT_STATE_EVENTS_STREAM_ORDERING_INDEX_UPDATE_NAME,
-            index_name="current_state_events_stream_ordering_idx",
-            table="current_state_events",
-            columns=["event_stream_ordering"],
-        )
-        self.db_pool.updates.register_background_index_update(
-            self.ROOM_MEMBERSHIPS_STREAM_ORDERING_INDEX_UPDATE_NAME,
-            index_name="room_memberships_stream_ordering_idx",
-            table="room_memberships",
-            columns=["event_stream_ordering"],
-        )
-        self.db_pool.updates.register_background_index_update(
-            self.LOCAL_CURRENT_MEMBERSHIP_STREAM_ORDERING_INDEX_UPDATE_NAME,
-            index_name="local_current_membership_stream_ordering_idx",
-            table="local_current_membership",
-            columns=["event_stream_ordering"],
-        )
-
     async def _background_deduplicate_state(
         self, progress: dict, batch_size: int
     ) -> int:
diff --git a/synapse/types/storage/__init__.py b/synapse/types/storage/__init__.py
index 378a15e038..b01653246a 100644
--- a/synapse/types/storage/__init__.py
+++ b/synapse/types/storage/__init__.py
@@ -38,6 +38,16 @@ class _BackgroundUpdates:
 
     EVENTS_JUMP_TO_DATE_INDEX = "events_jump_to_date_index"
 
+    CURRENT_STATE_EVENTS_STREAM_ORDERING_INDEX_UPDATE_NAME = (
+        "current_state_events_stream_ordering_idx"
+    )
+    ROOM_MEMBERSHIPS_STREAM_ORDERING_INDEX_UPDATE_NAME = (
+        "room_memberships_stream_ordering_idx"
+    )
+    LOCAL_CURRENT_MEMBERSHIP_STREAM_ORDERING_INDEX_UPDATE_NAME = (
+        "local_current_membership_stream_ordering_idx"
+    )
+
     SLIDING_SYNC_PREFILL_JOINED_ROOMS_TO_RECALCULATE_TABLE_BG_UPDATE = (
         "sliding_sync_prefill_joined_rooms_to_recalculate_table_bg_update"
     )