Set the room list mode synchronously on a warm launch

The room summary provider subscription only delivers its current state through an
async main queue hop, which can end up queued behind the first render. On a warm
launch, where the cached rooms have already been published before the home screen
exists, that leaves the skeletons up for the whole duration.

Read the current state at the end of init instead, alongside the rooms which were
already being read there.

UnitTests/Sources/HomeScreenViewModelTests.swift

@@ -384,6 +384,14 @@ final class HomeScreenViewModelTests {
     
     enum InviteType { case rooms, spaces }
     
+    @Test
+    func roomListModeIsSetSynchronouslyOnAWarmLaunch() {
+        setupViewModel()
+        
+        // No awaiting, the mode must not need the subscription's async delivery.
+        #expect(context.viewState.roomListMode == .rooms)
+    }
+    
     @Test
     func roomListModeWaitsForTheRoomsToPublish() async throws {
         let (roomListSubject, stateSubject) = setupViewModelWithManualProvider()