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)

apps/web-legacy/components/ui/input.tsx

@@ -0,0 +1,22 @@
+import * as React from 'react';
+
+import { cn } from '@/lib/utils';
+
+const Input = React.forwardRef<HTMLInputElement, React.InputHTMLAttributes<HTMLInputElement>>(
+  ({ className, type, ...props }, ref) => {
+    return (
+      <input
+        type={type}
+        className={cn(
+          'flex h-10 w-full rounded-md border border-input bg-background px-3 py-2 text-sm ring-offset-background file:border-0 file:bg-transparent file:text-sm file:font-medium file:text-foreground placeholder:text-muted-foreground focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-ring focus-visible:ring-offset-2 disabled:cursor-not-allowed disabled:opacity-50',
+          className
+        )}
+        ref={ref}
+        {...props}
+      />
+    );
+  }
+);
+Input.displayName = 'Input';
+
+export { Input };