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/components/DocsGPTChatWidget.jsx

@@ -0,0 +1,40 @@
+'use client';
+
+import dynamic from 'next/dynamic';
+import { useTheme } from 'next-themes';
+import { useEffect, useState } from 'react';
+
+// The widget reads window/navigator on mount and ships its own styled-components
+// trees, so it must never be prerendered.
+const DocsGPTWidget = dynamic(
+  () => import('docsgpt-react').then((mod) => mod.DocsGPTWidget),
+  { ssr: false },
+);
+
+const apiHost =
+  process.env.NEXT_PUBLIC_DOCSGPT_API_HOST || 'https://gptcloud.arc53.com';
+const apiKey = process.env.NEXT_PUBLIC_DOCSGPT_API_KEY;
+
+export function DocsGPTChatWidget() {
+  const { resolvedTheme } = useTheme();
+  const [mounted, setMounted] = useState(false);
+
+  useEffect(() => setMounted(true), []);
+
+  // No key means no widget. Falling through would silently use the demo key
+  // baked into the package default.
+  if (!apiKey || !mounted) return null;
+
+  return (
+    <DocsGPTWidget
+      apiHost={apiHost}
+      apiKey={apiKey}
+      theme={resolvedTheme === 'light' ? 'light' : 'dark'}
+      buttonText="Ask the docs"
+      title="Ask DocsGPT"
+      description="Answers drawn from these docs"
+      heroTitle="Ask anything about DocsGPT"
+      heroDescription="Answers are generated from this documentation. Check the sources for anything you plan to rely on."
+    />
+  );
+}