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>

docs/TASKS.md

@@ -29,7 +29,7 @@
 | P2-005 | done        | Phase 2   | @mosaic/coord — migrate from v0, gateway integration          | #77 | #23   |
 | P2-006 | done        | Phase 2   | Agent session management — tmux + monitoring                  | #78 | #24   |
 | P2-007 | done        | Phase 2   | Verify Phase 2 — multi-provider routing works                 | #79 | #25   |
-| P3-001 | not-started | Phase 3   | apps/web scaffold — Next.js 16 + BetterAuth + Tailwind        | —   | #26   |
+| P3-001 | in-progress | Phase 3   | apps/web scaffold — Next.js 16 + BetterAuth + Tailwind        | —   | #26   |
 | P3-002 | not-started | Phase 3   | Auth pages — login, registration, SSO redirect                | —   | #27   |
 | P3-003 | not-started | Phase 3   | Chat UI — conversations, messages, streaming                  | —   | #28   |
 | P3-004 | not-started | Phase 3   | Task management — list view + kanban board                    | —   | #29   |