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/src/routes/stripe-webhooks.ts

@@ -1,7 +1,7 @@
 import { Hono } from "hono";
 import Stripe from "stripe";
 import { z } from "zod/v3";
-import { eq, getDb, invoices } from "./packages/db";
+import { eq, getDb, invoices } from "../db";
 import { getStripeClient } from "../services/payment.js";
 
 export const webhooksRouter = new Hono();