website: add /cloud design partners page and shared shell

- New /cloud page with signup form (email, name, company, role, message)
  posting to a Discord webhook via a TanStack Start server function on
  the Cloudflare Worker. Webhook URL read from DISCORD_WEBHOOK_URL secret.
- Extract SiteShell, SiteFooter, FAQItem from landing-page.
- Migrate /privacy, /download, /blog, /changelog, /cloud to SiteShell so
  they share header + footer with consistent width.
- Add /cloud to header and footer nav.
- Make /docs sidebar full-width; bump footer text from xs to sm.
- Add Cloudflare Workers types and ignore .dev.vars.

packages/website/src/components/site-footer.tsx

@@ -0,0 +1,126 @@
+import { appStoreUrl, playStoreUrl, webAppUrl } from "~/downloads";
+
+interface SiteFooterProps {
+  width?: "default" | "prose";
+}
+
+export function SiteFooter({ width = "default" }: SiteFooterProps) {
+  const widthClasses =
+    width === "prose" ? "max-w-prose p-6 md:p-12 md:pt-0" : "max-w-5xl p-6 md:p-20 md:pt-0";
+  return (
+    <footer className={`${widthClasses} mx-auto`}>
+      <div className="border-t border-white/10 pt-8 pb-4 grid grid-cols-2 sm:grid-cols-4 gap-8 text-sm">
+        <div className="space-y-3">
+          <p className="text-white/60 font-medium">Product</p>
+          <div className="space-y-2">
+            <a href="/blog" className="block text-white/40 hover:text-white/60 transition-colors">
+              Blog
+            </a>
+            <a href="/docs" className="block text-white/40 hover:text-white/60 transition-colors">
+              Docs
+            </a>
+            <a
+              href="/changelog"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              Changelog
+            </a>
+            <a href="/cloud" className="block text-white/40 hover:text-white/60 transition-colors">
+              Cloud
+            </a>
+            <a
+              href="/docs/cli"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              CLI
+            </a>
+            <a
+              href="/privacy"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              Privacy
+            </a>
+          </div>
+        </div>
+        <div className="space-y-3">
+          <p className="text-white/60 font-medium">Agents</p>
+          <div className="space-y-2">
+            <a
+              href="/claude-code"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              Claude Code
+            </a>
+            <a href="/codex" className="block text-white/40 hover:text-white/60 transition-colors">
+              Codex
+            </a>
+            <a
+              href="/opencode"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              OpenCode
+            </a>
+          </div>
+        </div>
+        <div className="space-y-3">
+          <p className="text-white/60 font-medium">Community</p>
+          <div className="space-y-2">
+            <a
+              href="https://discord.gg/jz8T2uahpH"
+              target="_blank"
+              rel="noopener noreferrer"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              Discord
+            </a>
+            <a
+              href="https://github.com/getpaseo/paseo"
+              target="_blank"
+              rel="noopener noreferrer"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              GitHub
+            </a>
+          </div>
+        </div>
+        <div className="space-y-3">
+          <p className="text-white/60 font-medium">Download</p>
+          <div className="space-y-2">
+            <a
+              href={appStoreUrl}
+              target="_blank"
+              rel="noopener noreferrer"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              App Store
+            </a>
+            <a
+              href={playStoreUrl}
+              target="_blank"
+              rel="noopener noreferrer"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              Google Play
+            </a>
+            <a
+              href="https://github.com/getpaseo/paseo/releases"
+              target="_blank"
+              rel="noopener noreferrer"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              Desktop
+            </a>
+            <a
+              href={webAppUrl}
+              target="_blank"
+              rel="noopener noreferrer"
+              className="block text-white/40 hover:text-white/60 transition-colors"
+            >
+              Web App
+            </a>
+          </div>
+        </div>
+      </div>
+    </footer>
+  );
+}