refactor: inline packages/db and packages/types into api package

Phase 2 extraction: groombook/api from groombook/app monorepo.

Changes:
- Move packages/db content to apps/api/src/db/
- Move packages/types content to apps/api/src/types/
- Inline database schema and migrations into api package
- Update Dockerfile to build single package
- Update CI workflow for single-package structure
- Fix vitest.config.ts aliases

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/api/drizzle.config.ts

@@ -0,0 +1,10 @@
+import { defineConfig } from "drizzle-kit";
+
+export default defineConfig({
+  schema: "./src/schema.ts",
+  out: "./migrations",
+  dialect: "postgresql",
+  dbCredentials: {
+    url: process.env.DATABASE_URL!,
+  },
+});