refactor: rebuild template — Tailwind v4, Docker self-hosting, passkey auth

Toolchain fixes (all previously broken):
- npm run lint: next lint was removed in Next 16 -> eslint with flat config
- .eslintrc.json was ignored by ESLint 9 -> eslint.config.mjs
- npm test / test:e2e exited 1 with no tests -> passWithNoTests
- Vitest scanned tests/ and would have run Playwright specs -> scoped to src/
- Playwright targeted Mobile Safari while docs installed only chromium
- reuseExistingServer silently tested a foreign server on :3000 -> E2E_PORT
- 11 high-severity vulns -> npm audit fix
- deny rule Read(**/.env*) also blocked .env.example -> precise patterns

Stack changes:
- Tailwind v3 -> v4 (CSS-first, no tailwind.config.ts, tw-animate-css)
- shadcn regenerated for v4; 33 components -> 6 core, bundled radix-ui
- Supabase removed entirely; data layer is now chosen per project
- Vercel removed; Docker Compose self-hosting with scripts/update.sh
- Better Auth + passkey plugin as the binding auth standard
- ThemeProvider and Sonner mounted; dark mode and toasts now actually work

Workflow system:
- Sub-agents wired: /frontend, /backend, /qa delegate to .claude/agents
- Checklists folded into their SKILL.md; one file per skill
- Rules rewritten: DB-agnostic backend, passkey security, v4 frontend
- Spec language settled as German, skill instructions English

.env.example

@@ -0,0 +1,21 @@
+# Copy to .env and fill in. .env is gitignored and never committed.
+# Every variable the app needs must be listed here with a dummy value.
+
+# --- Application -------------------------------------------------------------
+# Public base URL of the deployment. Better Auth derives the WebAuthn
+# relying-party ID from this hostname — a wrong value makes every passkey
+# fail verification, so keep it in sync with the domain you serve from.
+NEXT_PUBLIC_APP_URL=http://localhost:3000
+
+# --- Docker Compose ----------------------------------------------------------
+APP_NAME=ai-coding-starter
+APP_PORT=3000
+# Keep on loopback: the reverse proxy on the host forwards to this port.
+APP_BIND=127.0.0.1
+
+# --- Auth (only when the project uses authentication) ------------------------
+# BETTER_AUTH_SECRET=generate_with_openssl_rand_base64_32
+# BETTER_AUTH_URL=http://localhost:3000
+
+# --- Database (chosen per project by /architecture) --------------------------
+# DATABASE_URL=postgres://user:password@db:5432/app