feat(docs): mount the DocsGPT chat widget

Adds a floating "Ask the docs" bubble to every docs page. docsgpt-react
was already a dependency but nothing imported it, so no widget rendered.

The widget reads window and navigator on mount, so it is lazy-loaded
with ssr: false from a client wrapper. Its light/dark theme follows the
site toggle via next-themes, promoted here from a transitive dependency
to a declared one.

The key comes from NEXT_PUBLIC_DOCSGPT_API_KEY and the host from
NEXT_PUBLIC_DOCSGPT_API_HOST. With no key set the wrapper renders
nothing rather than falling through to the demo key the package defaults
to.

Bumping docsgpt-react to ^0.7.0 also drops a duplicate React. The old
^0.6.3 pin depended on React 18 and npm installed a nested 18.3.1 beside
the app's 19.2.8, which would have thrown an invalid hook call on first
render.

docs/package.json

@@ -8,8 +8,9 @@
   "license": "MIT",
   "dependencies": {
     "@vercel/analytics": "^2.0.1",
-    "docsgpt-react": "^0.6.3",
+    "docsgpt-react": "^0.7.0",
     "next": "^16.3.0",
+    "next-themes": "^0.4.6",
     "nextra": "^4.6.1",
     "nextra-theme-docs": "^4.6.1",
     "react": "^19.2.8",