fix: keep install assets inside a non-root base

Manifest start_url, scope and icon src resolve against the manifest URL,
so root-relative values sent an app served under a path prefix to the
domain root. Make them relative, and add a build test under
base: '/example/' that asserts every emitted link and manifest URL stays
inside the base. index.html is unchanged: Vite already rewrites its
links under base.

public/manifest.webmanifest

@@ -2,17 +2,17 @@
   "name": "God's Eye View",
   "short_name": "God's Eye",
   "description": "Live spatial intelligence in the browser.",
-  "start_url": "/",
-  "scope": "/",
+  "start_url": ".",
+  "scope": ".",
   "display": "standalone",
   "orientation": "any",
   "background_color": "#0a0a0f",
   "theme_color": "#0a0a0f",
   "icons": [
-    { "src": "/icons/icon-192.png", "sizes": "192x192", "type": "image/png" },
-    { "src": "/icons/icon-512.png", "sizes": "512x512", "type": "image/png" },
+    { "src": "icons/icon-192.png", "sizes": "192x192", "type": "image/png" },
+    { "src": "icons/icon-512.png", "sizes": "512x512", "type": "image/png" },
     {
-      "src": "/icons/icon-512-maskable.png",
+      "src": "icons/icon-512-maskable.png",
       "sizes": "512x512",
       "type": "image/png",
       "purpose": "maskable"