Add Sliding Sync `/sync` endpoint (initial implementation) (#17187)

Based on [MSC3575](https://github.com/matrix-org/matrix-spec-proposals/pull/3575): Sliding Sync

This iteration only focuses on returning the list of room IDs in the sliding window API (without sorting/filtering).

Rooms appear in the Sliding sync response based on:

 - `invite`, `join`, `knock`, `ban` membership events
 - Kicks (`leave` membership events where `sender` is different from the `user_id`/`state_key`)
 - `newly_left` (rooms that were left during the given token range, > `from_token` and <= `to_token`)
 - In order for bans/kicks to not show up, you need to `/forget` those rooms. This doesn't modify the event itself though and only adds the `forgotten` flag to `room_memberships` in Synapse. There isn't a way to tell when a room was forgotten at the moment so we can't factor it into the from/to range.

### Example request

`POST http://localhost:8008/_matrix/client/unstable/org.matrix.msc3575/sync`

```json
{
  "lists": {
    "foo-list": {
      "ranges": [ [0, 99] ],
      "sort": [ "by_notification_level", "by_recency", "by_name" ],
      "required_state": [
        ["m.room.join_rules", ""],
        ["m.room.history_visibility", ""],
        ["m.space.child", "*"]
      ],
      "timeline_limit": 100
    }
  }
}
```

Response:
```json
{
  "next_pos": "s58_224_0_13_10_1_1_16_0_1",
  "lists": {
    "foo-list": {
      "count": 1,
      "ops": [
        {
          "op": "SYNC",
          "range": [0, 99],
          "room_ids": [
            "!MmgikIyFzsuvtnbvVG:my.synapse.linux.server"
          ]
        }
      ]
    }
  },
  "rooms": {},
  "extensions": {}
}
```

1 files changed, 11 insertions, 8 deletions

diff --git a/synapse/handlers/sync.py b/synapse/handlers/sync.py
index 9d37e2a86f..39964726c5 100644
--- a/synapse/handlers/sync.py
+++ b/synapse/handlers/sync.py
@@ -2002,7 +2002,7 @@ class SyncHandler:
         """
         user_id = sync_config.user.to_string()
 
-        # Note: we get the users room list *before* we get the current token, this
+        # Note: we get the users room list *before* we get the `now_token`, this
         # avoids checking back in history if rooms are joined after the token is fetched.
         token_before_rooms = self.event_sources.get_current_token()
         mutable_joined_room_ids = set(await self.store.get_rooms_for_user(user_id))
@@ -2014,10 +2014,10 @@ class SyncHandler:
         now_token = self.event_sources.get_current_token()
         log_kv({"now_token": now_token})
 
-        # Since we fetched the users room list before the token, there's a small window
-        # during which membership events may have been persisted, so we fetch these now
-        # and modify the joined room list for any changes between the get_rooms_for_user
-        # call and the get_current_token call.
+        # Since we fetched the users room list before calculating the `now_token` (see
+        # above), there's a small window during which membership events may have been
+        # persisted, so we fetch these now and modify the joined room list for any
+        # changes between the get_rooms_for_user call and the get_current_token call.
         membership_change_events = []
         if since_token:
             membership_change_events = await self.store.get_membership_changes_for_user(
@@ -2027,16 +2027,19 @@ class SyncHandler:
                 self.rooms_to_exclude_globally,
             )
 
-            mem_last_change_by_room_id: Dict[str, EventBase] = {}
+            last_membership_change_by_room_id: Dict[str, EventBase] = {}
             for event in membership_change_events:
-                mem_last_change_by_room_id[event.room_id] = event
+                last_membership_change_by_room_id[event.room_id] = event
 
             # For the latest membership event in each room found, add/remove the room ID
             # from the joined room list accordingly. In this case we only care if the
             # latest change is JOIN.
 
-            for room_id, event in mem_last_change_by_room_id.items():
+            for room_id, event in last_membership_change_by_room_id.items():
                 assert event.internal_metadata.stream_ordering
+                # As a shortcut, skip any events that happened before we got our
+                # `get_rooms_for_user()` snapshot (any changes are already represented
+                # in that list).
                 if (
                     event.internal_metadata.stream_ordering
                     < token_before_rooms.room_key.stream