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/0008_business_settings.sql

@@ -0,0 +1,15 @@
+CREATE TABLE IF NOT EXISTS "business_settings" (
+  "id" uuid PRIMARY KEY DEFAULT gen_random_uuid() NOT NULL,
+  "business_name" text DEFAULT 'GroomBook' NOT NULL,
+  "logo_base64" text,
+  "logo_mime_type" text,
+  "primary_color" text DEFAULT '#4f8a6f' NOT NULL,
+  "accent_color" text DEFAULT '#8b7355' NOT NULL,
+  "created_at" timestamp DEFAULT now() NOT NULL,
+  "updated_at" timestamp DEFAULT now() NOT NULL
+);
+
+-- Seed a default row so GET always returns something
+INSERT INTO "business_settings" ("business_name", "primary_color", "accent_color")
+VALUES ('GroomBook', '#4f8a6f', '#8b7355')
+ON CONFLICT DO NOTHING;