feat(web): scaffold Next.js 16 dashboard with design system and auth client

Build out apps/web with Tailwind CSS v4, BetterAuth client, and the Mosaic
design system. Populate @mosaic/design-tokens with actual color palette
(deep blue-grays, blue/purple/teal accents), font definitions (Outfit/Fira Code),
and spacing scale per AD-13.

- Tailwind v4 CSS-first config with @theme tokens in globals.css
- next/font for self-hosted Outfit + Fira Code (no Google CDN)
- App shell with sidebar nav, topbar, and content area
- Route groups: (dashboard) with AppShell, (auth) with centered card
- Placeholder pages: /chat, /login, /register
- BetterAuth React client (useSession, signIn, signUp, signOut)
- Gateway API fetch wrapper with credentials
- cn() utility with clsx + tailwind-merge
- Dark theme default, WCAG-friendly contrast

Refs #26

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/web/postcss.config.mjs

@@ -0,0 +1,8 @@
+/** @type {import('postcss-load-config').Config} */
+const config = {
+  plugins: {
+    '@tailwindcss/postcss': {},
+  },
+};
+
+export default config;