Add MatrixClient.totalUnreadCountFlow() extension

Extract the logic to observe the total unread count of a MatrixClient, refreshed on each sync
heartbeat, to a shared extension and use it in HomePresenter and PreferencesRootPresenter.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

libraries/matrix/api/src/main/kotlin/io/element/android/libraries/matrix/api/MatrixClient.kt

@@ -51,9 +51,15 @@ import io.element.android.libraries.matrix.api.user.UserStatus
 import io.element.android.libraries.matrix.api.verification.SessionVerificationService
 import kotlinx.collections.immutable.ImmutableList
 import kotlinx.coroutines.CoroutineScope
+import kotlinx.coroutines.FlowPreview
 import kotlinx.coroutines.flow.Flow
 import kotlinx.coroutines.flow.StateFlow
+import kotlinx.coroutines.flow.debounce
+import kotlinx.coroutines.flow.distinctUntilChanged
+import kotlinx.coroutines.flow.map
+import kotlinx.coroutines.flow.onStart
 import java.util.Optional
+import kotlin.time.Duration.Companion.milliseconds
 
 /**
  * Entry point for everything scoped to a single logged in session: the sub-services, room access, and account level operations.
@@ -523,3 +529,18 @@ fun MatrixClient.roomAliasFromName(name: String): RoomAlias? {
         ?.takeIf { MatrixPatterns.isRoomAlias(it) }
         ?.let { tryOrNull { RoomAlias(it) } }
 }
+
+/**
+ * Returns a flow of the total number of unread notifications across all rooms.
+ * The first value is emitted immediately, then the value is refreshed on each sync heartbeat.
+ * In case of error, 0 is emitted.
+ */
+@OptIn(FlowPreview::class)
+fun MatrixClient.totalUnreadCountFlow(): Flow<Int> {
+    return syncService.heartBeat
+        // Delay the heartbeat so the SDK has time to update the unread count before we read it.
+        .debounce(100.milliseconds)
+        .onStart { emit(Unit) }
+        .map { totalUnreadCount().getOrDefault(0).toInt() }
+        .distinctUntilChanged()
+}