T1/Phase 1: scaffold Vite SPA + Hono API + Bun worker

- apps/web: Vite + React 19 + TanStack Router/Query + shadcn/ui
   - apps/api: Hono + Bun on :3001 with /api/health, /api/auth/*, /mcp stubs
   - apps/worker: Bun worker stub, DB connection, graceful SIGTERM
   - apps/web-legacy/: old Next.js code moved aside (preserved for T2-T8 reference)
   - Dockerfiles: api (Bun), worker (Bun), spa (multi-stage Caddy)
   - Caddyfile: serves dist + reverse-proxies /api/* + /mcp to api
   - docker-compose.yml: 4-service target (api, spa, db, worker)
   - packages/db/src/client.ts: shared Drizzle client for api + worker
   - db/client.ts: root-level alias for convenience

   Parent: t_e1cbd87d -> t_24c9c3fd (T0)

Dockerfile.api

@@ -0,0 +1,19 @@
+FROM oven/bun:1.3 AS base
+WORKDIR /app
+
+# Copy workspace manifests
+COPY package.json bunfig.toml ./
+COPY apps/api/package.json apps/api/
+COPY packages/db/package.json packages/db/
+COPY packages/shared/package.json packages/shared/
+
+# Install dependencies (Bun workspace-aware)
+RUN bun install --production --frozen-lockfile 2>/dev/null || bun install --production
+
+# Copy source code
+COPY apps/api/src ./apps/api/src
+COPY db ./db
+COPY packages/db/src ./packages/db/src
+COPY packages/shared/src ./packages/shared/src
+
+CMD ["bun", "run", "apps/api/src/index.ts"]