feat: add BASE_PATH env var for serving UI from a subpath

When BASE_PATH is set (e.g., /server/), the entrypoint script injects
a <base> tag and rewrites asset paths in index.html. React Router reads
the basename from the <base> tag. Vite builds with relative paths.
Default / for standalone mode (no changes).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

ui/src/router.tsx

@@ -41,6 +41,8 @@ function LegacyAgentRedirect() {
   return <Navigate to={path} replace />;
 }
 
+const basename = document.querySelector('base')?.getAttribute('href')?.replace(/\/$/, '') || '';
+
 export const router = createBrowserRouter([
   { path: '/login', element: <LoginPage /> },
   { path: '/oidc/callback', element: <OidcCallback /> },
@@ -101,4 +103,4 @@ export const router = createBrowserRouter([
       },
     ],
   },
-]);
+], { basename: basename || undefined });