Initial extraction: groombook/api from groombook/app monorepo

Part of GRO-802 monorepo breakdown.

Changes:
- Extract apps/api/ as the main API service
- Inline packages/db/ (database schema, migrations, utilities)
- Inline packages/types/ (shared TypeScript types)
- Add CI workflow for lint, typecheck, test, build, docker
- Port Dockerfile with 4 stages: runner, migrate, seed, reset

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

.env.example

@@ -0,0 +1,36 @@
+# Groom Book — Environment Variables
+# Copy this file to .env and adjust values for your deployment.
+
+# ── Database ──────────────────────────────────────────────────────────────────
+DATABASE_URL=postgres://groombook:groombook@postgres:5432/groombook
+
+# ── Authentication ────────────────────────────────────────────────────────────
+# Set AUTH_DISABLED=true to skip OIDC validation (useful for local dev/Docker).
+# In production, configure an Authentik instance and set these values.
+AUTH_DISABLED=false
+OIDC_ISSUER=https://authentik.example.com
+OIDC_AUDIENCE=groombook
+
+# ── Setup Wizard ─────────────────────────────────────────────────────────────
+# When SKIP_OOBE=true, the setup wizard is bypassed regardless of whether a
+# super user exists in the database. Useful in dev/test environments where the
+# database has data but the setup wizard would otherwise block access.
+SKIP_OOBE=false
+
+# ── API ───────────────────────────────────────────────────────────────────────
+PORT=3000
+CORS_ORIGIN=http://localhost:8080
+
+# ── Email Reminders (optional) ────────────────────────────────────────────────
+# Leave SMTP_HOST unset to disable email notifications entirely.
+# When configured, appointment confirmation and reminder emails are sent via SMTP.
+SMTP_HOST=smtp.example.com
+SMTP_PORT=587
+SMTP_SECURE=false
+SMTP_USER=user@example.com
+SMTP_PASS=password
+SMTP_FROM="Groom Book <noreply@example.com>"
+
+# Hours before appointment to send reminder emails (defaults: 24 and 2)
+REMINDER_HOURS_EARLY=24
+REMINDER_HOURS_LATE=2