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/0007_tip_splitting.sql

@@ -0,0 +1,25 @@
+-- Add bather/assistant staff tracking to appointments and tip split ledger (closes groombook/groombook#12)
+
+-- Secondary staff member (e.g., bather) who assisted the primary groomer
+ALTER TABLE "appointments"
+  ADD COLUMN "bather_staff_id" uuid REFERENCES "public"."staff"("id") ON DELETE set null ON UPDATE no action;
+--> statement-breakpoint
+
+-- Stores per-staff tip allocations calculated when an invoice is paid
+CREATE TABLE "invoice_tip_splits" (
+  "id" uuid PRIMARY KEY DEFAULT gen_random_uuid() NOT NULL,
+  "invoice_id" uuid NOT NULL,
+  "staff_id" uuid,
+  "staff_name" text NOT NULL,
+  "share_pct" numeric(5, 2) NOT NULL,
+  "share_cents" integer NOT NULL,
+  "created_at" timestamp DEFAULT now() NOT NULL
+);
+--> statement-breakpoint
+ALTER TABLE "invoice_tip_splits"
+  ADD CONSTRAINT "invoice_tip_splits_invoice_id_invoices_id_fk"
+    FOREIGN KEY ("invoice_id") REFERENCES "public"."invoices"("id") ON DELETE cascade ON UPDATE no action;
+--> statement-breakpoint
+ALTER TABLE "invoice_tip_splits"
+  ADD CONSTRAINT "invoice_tip_splits_staff_id_staff_id_fk"
+    FOREIGN KEY ("staff_id") REFERENCES "public"."staff"("id") ON DELETE set null ON UPDATE no action;