feat(webui): add health check monitoring for connection status

Implement periodic health checks every 15 seconds to monitor connection status,
pausing when the tab is hidden and resuming on visibility. Update UI bindings
to use data store for connection status instead of global store. Add destroy
method to clean up timers on component teardown.

public/js/app-init.js

@@ -34,7 +34,7 @@ document.addEventListener('alpine:init', () => {
             this.startAutoRefresh();
             document.addEventListener('refresh-interval-changed', () => this.startAutoRefresh());
 
-            // Initial Fetch
+            // Initial Data Fetch (separate from health check)
             Alpine.store('data').fetchData();
         },