refactor(myTischtennis): streamline session management and enhance login flow

- Updated AutoFetchMatchResultsService to utilize verifyLogin for session re-establishment, improving reliability and handling of CAPTCHA challenges.
- Refactored MyTischtennisService to save Playwright storage state separately, ensuring robustness in session persistence and preventing failures due to missing DB columns.
- Minor adjustments in TeamManagementView to enhance async data fetching logic.

frontend/src/views/TeamManagementView.vue

@@ -1176,6 +1176,7 @@ export default {
       myTischtennisSuccess.value = '';
       
       try {
+
         const startResponse = await apiClient.post('/mytischtennis/fetch-team-data/async', {
           clubTeamId: teamToEdit.value.id
         });