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

tests/smoke.spec.ts

@@ -0,0 +1,17 @@
+import { expect, test } from '@playwright/test'
+
+// Playwright specs live here and must never be picked up by Vitest —
+// vitest.config.ts scopes itself to src/ for exactly that reason.
+
+test('start page renders', async ({ page }) => {
+  await page.goto('/')
+  await expect(
+    page.getByRole('heading', { name: 'AI Coding Starter Kit' })
+  ).toBeVisible()
+})
+
+test('health endpoint answers', async ({ request }) => {
+  const response = await request.get('/api/health')
+  expect(response.ok()).toBe(true)
+  expect(await response.json()).toEqual({ status: 'ok' })
+})