Extract groombook/api from monorepo with CI workflow

- Add source code from apps/api
- Add packages/db and packages/types workspace dependencies
- Add GitHub Actions CI workflow (lint, typecheck, test, docker)
- Generate pnpm-lock.yaml
- Add .gitignore

Co-Authored-By: Paperclip <noreply@paperclip.ing>

packages/db/migrations/0005_appointment_groups.sql

@@ -0,0 +1,12 @@
+-- Appointment groups: link multiple appointments from the same client visit.
+-- Each appointment in a group is for a different pet and may have a different groomer.
+CREATE TABLE appointment_groups (
+  id UUID PRIMARY KEY DEFAULT gen_random_uuid(),
+  client_id UUID NOT NULL REFERENCES clients(id) ON DELETE RESTRICT,
+  notes TEXT,
+  created_at TIMESTAMP NOT NULL DEFAULT NOW(),
+  updated_at TIMESTAMP NOT NULL DEFAULT NOW()
+);
+
+-- Link appointments to a group (nullable — non-grouped appointments are unaffected)
+ALTER TABLE appointments ADD COLUMN group_id UUID REFERENCES appointment_groups(id) ON DELETE SET NULL;