Show the unread notification count on the chats tab

Set the chats tab's badge count from the same value used for the app badge.
The tab bar already renders it through the .badge modifier but that has no
effect outside of a TabView or List, so the iPad tab rail now overlays a
small NotificationCountBadge instead.

ElementX/Sources/Application/Navigation/NavigationTabCoordinator.swift

@@ -447,7 +447,12 @@ struct TabRailView<Tag: Hashable>: View {
                     }
                     .buttonStyle(TabButtonStyle(isSelected: isSelected))
                     .accessibilityAddTraits(isSelected ? .isSelected : [])
-                    .badge(10) // TODO: Check if this works.
+                    .overlay(alignment: .topTrailing) {
+                        if module.details.badgeCount > 0 {
+                            NotificationCountBadge(count: module.details.badgeCount, size: .small)
+                                .allowsHitTesting(false)
+                        }
+                    }
                 }
             }
             .padding(.horizontal, 8)

ElementX/Sources/FlowCoordinators/UserSessionFlowCoordinator.swift

@@ -540,6 +540,8 @@ class UserSessionFlowCoordinator: FlowCoordinatorProtocol {
                 
                 let badgeCount = Int(userSession.clientProxy.totalUnreadNotifications)
                 
+                chatsTabDetails.badgeCount = badgeCount
+                
                 await flowParameters.notificationManager.removeDeliveredNotificationsForFullyReadRooms(roomSummaries)
                 await flowParameters.notificationManager.updateAppBadgeCount(badgeCount)
             }