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/0023_auth_provider_config.sql

@@ -0,0 +1,14 @@
+CREATE TABLE "auth_provider_config" (
+	"id" uuid PRIMARY KEY DEFAULT gen_random_uuid() NOT NULL,
+	"provider_id" text NOT NULL,
+	"display_name" text NOT NULL,
+	"issuer_url" text NOT NULL,
+	"internal_base_url" text,
+	"client_id" text NOT NULL,
+	"client_secret" text NOT NULL,
+	"scopes" text DEFAULT 'openid profile email' NOT NULL,
+	"enabled" boolean DEFAULT true NOT NULL,
+	"created_at" timestamp DEFAULT now() NOT NULL,
+	"updated_at" timestamp DEFAULT now() NOT NULL,
+	CONSTRAINT "auth_provider_config_provider_id_unique" UNIQUE("provider_id")
+);