feat(web): SPA shell — gate, settings, today placeholder

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

web/index.html

@@ -0,0 +1,12 @@
+<!doctype html>
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1" />
+    <title>Helios</title>
+  </head>
+  <body>
+    <div id="root"></div>
+    <script type="module" src="/src/main.tsx"></script>
+  </body>
+</html>