chore: Follow up homeserverpicker UX

lib/pages/homeserver_picker/homeserver_picker.dart

@@ -73,12 +73,18 @@ class HomeserverPickerController extends State<HomeserverPicker> {
     );
   }
 
-  tryCheckHomeserverActionWithoutCooldown([_]) {
+  void tryCheckHomeserverActionWithoutCooldown([_]) {
     _checkHomeserverCooldown?.cancel();
     _lastCheckedUrl = null;
     checkHomeserverAction();
   }
 
+  void onSubmitted([_]) {
+    if (supportsSso) return ssoLoginAction();
+    if (supportsPasswordLogin) return login();
+    return tryCheckHomeserverActionWithoutCooldown();
+  }
+
   /// Starts an analysis of the given homeserver. It uses the current domain and
   /// makes sure that it is prefixed with https. Then it searches for the
   /// well-known information and forwards to the login page depending on the

lib/pages/homeserver_picker/homeserver_picker_view.dart

@@ -137,10 +137,7 @@ class HomeserverPickerView extends StatelessWidget {
                           TextField(
                             onChanged:
                                 controller.tryCheckHomeserverActionWithCooldown,
-                            onEditingComplete: controller
+                            onSubmitted: controller.onSubmitted,
-                                .tryCheckHomeserverActionWithoutCooldown,
-                            onSubmitted: controller
-                                .tryCheckHomeserverActionWithoutCooldown,
                             onTap:
                                 controller.tryCheckHomeserverActionWithCooldown,
                             controller: controller.homeserverController,