fix: restore and stabilize tab navigation with Alpine.js

- Fixed navigation blockage by moving Alpine state to body scope
- Resolved CSS display conflicts between legacy .active class and x-show
- Synchronized legacy auth logic with Alpine global state
- Redirected legacy switchTab calls to Alpine events
- Removed obsolete tabs.js and updated home section initialization
- Added E2E navigation test placeholder

templates/base.html

@@ -23,7 +23,6 @@
     <script src="/static/js/anime-details.js?v=1.12" defer></script>
     <script src="/static/js/series-search.js?v=1.11" defer></script>
     <script src="/static/js/recommendations.js?v=1.11" defer></script>
-    <script src="/static/js/tabs.js?v=1.11" defer></script>
     <script src="/static/js/watchlist.js?v=1.11" defer></script>
     <script src="/static/js/watchlist-ui.js?v=1.11" defer></script>
     <script src="/static/js/main.js?v=1.11" defer></script>