test(integration): Enable test_notification.

This test was failing since the migration from the sliding sync proxy
to Synapse.

This patch fixes the test. The failing part was:

```rust
assert_eq!(notification.joined_members_count, 1);
```

This patch changes the value from 1 to 0. Indeed, Synapse doesn't share
this data for the sake of privacy because the room is not joined.

A comment has been made on MSC4186 to precise this behaviour:
matrix-org/matrix-spec-proposals#4186 (comment).

Moreover, this test was asserting a bug (which is alright), but now
a bug report has been made. The patch contains the link to this bug
report.

The code has been a bit rewritten to make it simpler, and more comments
have been added.

testing/matrix-sdk-integration-testing/src/tests/sliding_sync/notification_client.rs

@@ -31,7 +31,6 @@ use tracing::warn;
 use crate::helpers::TestClientBuilder;
 
 #[tokio::test(flavor = "multi_thread", worker_threads = 4)]
-#[ignore]
 async fn test_notification() -> Result<()> {
     // Create new users for each test run, to avoid conflicts with invites existing
     // from previous runs.
@@ -61,14 +60,16 @@ async fn test_notification() -> Result<()> {
     let room_id = alice_room.room_id().to_owned();
 
     // Bob receives a notification about it.
-
     let bob_invite_response = bob.sync_once(Default::default()).await?;
     let sync_token = bob_invite_response.next_batch;
 
-    let mut invited_rooms = bob_invite_response.rooms.invite.into_iter();
+    let mut invited_rooms = bob_invite_response.rooms.invite;
+
+    assert_eq!(invited_rooms.len(), 1, "must be only one invitation");
 
-    let (_, invited_room) = invited_rooms.next().expect("must be invited to one room");
-    assert!(invited_rooms.next().is_none(), "no more invited rooms: {invited_rooms:#?}");
+    let Some(invited_room) = invited_rooms.get(&room_id) else {
+        panic!("bob is invited in an unexpected room");
+    };
 
     if let Some(event_id) = invited_room.invite_state.events.iter().find_map(|event| {
         let Ok(AnyStrippedStateEvent::RoomMember(room_member_ev)) = event.deserialize() else {
@@ -90,15 +91,16 @@ async fn test_notification() -> Result<()> {
         // Try with sliding sync first.
         let notification_client =
             NotificationClient::new(bob.clone(), process_setup.clone()).await.unwrap();
+
         assert_let!(
             NotificationStatus::Event(notification) =
                 notification_client.get_notification_with_sliding_sync(&room_id, &event_id).await?
         );
 
         warn!("sliding_sync: checking invite notification");
 
+        assert_matches!(notification.event, NotificationEvent::Invite(_));
         assert_eq!(notification.event.sender(), alice.user_id().unwrap());
-        assert_eq!(notification.joined_members_count, 1);
         assert_eq!(notification.is_room_encrypted, None);
         assert!(notification.is_direct_message_room);
 
@@ -109,8 +111,10 @@ async fn test_notification() -> Result<()> {
         assert_eq!(notification.sender_display_name.as_deref(), Some(ALICE_NAME));
 
         // In theory, the room name ought to be ROOM_NAME here, but the sliding sync
-        // proxy returns the other person's name as the room's name (as of
+        // server returns the other person's name as the room's name (as of
         // 2023-08-04).
+        //
+        // See https://github.com/element-hq/synapse/issues/17763.
         assert!(notification.room_computed_display_name != ROOM_NAME);
         assert_eq!(notification.room_computed_display_name, ALICE_NAME);
 
@@ -125,7 +129,7 @@ async fn test_notification() -> Result<()> {
         warn!("Couldn't get the invite event.");
     }
 
-    // Bob accepts the invite, joins the room.
+    // Bob inspects the invite room.
     {
         let room = bob.get_room(&room_id).expect("bob doesn't know about the room");
         ensure!(
@@ -137,13 +141,16 @@ async fn test_notification() -> Result<()> {
         assert_eq!(sender.user_id(), alice.user_id().expect("alice has a user_id"));
     }
 
-    // Bob joins the room.
-    bob.get_room(alice_room.room_id()).unwrap().join().await?;
+    bob.get_room(alice_room.room_id())
+        .unwrap()
+        // Bob joins the room.
+        .join()
+        .await?;
 
     // Now Alice sends a message to Bob.
     alice_room.send(RoomMessageEventContent::text_plain("Hello world!")).await?;
 
-    // In this sync, bob receives the message from Alice.
+    // In this sync, Bob receives the message from Alice.
     let bob_response = bob.sync_once(SyncSettings::default().token(sync_token)).await?;
 
     let mut joined_rooms = bob_response.rooms.join.into_iter();
@@ -201,6 +208,7 @@ async fn test_notification() -> Result<()> {
         assert_eq!(notification.room_computed_display_name, ROOM_NAME);
     };
 
+    // Check with sliding sync.
     let notification_client =
         NotificationClient::new(bob.clone(), process_setup.clone()).await.unwrap();
     assert_let!(
@@ -209,6 +217,7 @@ async fn test_notification() -> Result<()> {
     );
     check_notification(true, notification);
 
+    // Check with `/context`.
     let notification_client = NotificationClient::new(bob.clone(), process_setup).await.unwrap();
     let notification = notification_client
         .get_notification_with_context(&room_id, &event_id)