webui: Fix demo page

- Change asset root for vite
- Update mock handlers to support SSE by replacing long polling implementation with Server-Sent Events (SSE) in webui mock handlers.

Co-Authored-By: sketch <hello@sketch.dev>
diff --git a/webui/vite.config.mts b/webui/vite.config.mts
index 2d99b63..9765931 100644
--- a/webui/vite.config.mts
+++ b/webui/vite.config.mts
@@ -33,7 +33,7 @@
     middlewareMode: false,
     fs: {
       // Allow serving files from these directories
-      allow: ["/app/webui"],
+      allow: ["."],
     },
   },
 });