Run the whole stack in Docker

- API and web images built with turbo prune; the API image also runs the
  worker and migrations. Non-root, health-checked, Debian slim.
- docker compose up -d --build starts Postgres, Redis (persistent), a
  one-shot migrate job, API, worker and web, in dependency order.
- Fix the API production build (tsup flags moved to a config file) and
  bundle the migration script; silence Postgres NOTICE noise.
- npm run infra:up now starts only Postgres and Redis for hot-reload dev.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01MzFywujuH9TiuXbr9vjoX8

apps/api/tsup.config.ts

@@ -0,0 +1,11 @@
+import { defineConfig } from 'tsup';
+
+export default defineConfig({
+  entry: ['src/server.ts', 'src/worker.ts', 'src/db/migrate.ts'],
+  format: ['esm'],
+  target: 'node22',
+  platform: 'node',
+  clean: true,
+  // The shared package ships TypeScript source, so bundle it; everything else stays in node_modules.
+  noExternal: ['@musicshare/shared'],
+});