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/migrations/0025_rate_limit.sql

@@ -0,0 +1,6 @@
+-- Better-Auth rate limiting table (GRO-574)
+CREATE TABLE "rate_limit" (
+  key TEXT NOT NULL PRIMARY KEY,
+  count INTEGER NOT NULL,
+  last_request BIGINT NOT NULL
+);