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/app/layout.jsx

@@ -5,6 +5,7 @@ import { getPageMap } from 'nextra/page-map';
 import { Footer, Layout, Navbar } from 'nextra-theme-docs';
 import 'nextra-theme-docs/style.css';
 
+import { DocsGPTChatWidget } from '../components/DocsGPTChatWidget';
 import CuteLogo from '../public/cute-docsgpt.png';
 import themeConfig from '../theme.config';
 
@@ -79,6 +80,7 @@ export default async function RootLayout({ children }) {
         >
           {children}
         </Layout>
+        <DocsGPTChatWidget />
         <Analytics />
       </body>
     </html>