Store the first provider even if no distributor is available, else error in troubleshoot test will not be accurate.

Also when registering for the first time, pick the fist available provider with at least one distributor.

libraries/push/impl/src/main/kotlin/io/element/android/libraries/push/impl/DefaultPushService.kt

@@ -73,6 +73,15 @@ class DefaultPushService @Inject constructor(
         return pushProvider.registerWith(matrixClient, distributor)
     }
 
+    override suspend fun selectPushProvider(
+        matrixClient: MatrixClient,
+        pushProvider: PushProvider,
+    ) {
+        Timber.d("Select ${pushProvider.name}")
+        val userPushStore = userPushStoreFactory.getOrCreate(matrixClient.sessionId)
+        userPushStore.setPushProviderName(pushProvider.name)
+    }
+
     override fun ignoreRegistrationError(sessionId: SessionId): Flow<Boolean> {
         return userPushStoreFactory.getOrCreate(sessionId).ignoreRegistrationError()
     }