refactor(backend): clean up router registration pattern

Issue #6: Multiple routers per file made main.py verbose.

Changes:
- Add 'routers' list export to booking.py and invites.py
- Update main.py to iterate over router lists for multi-router modules
- Keep explicit registration for single-router modules
- Cleaner separation between simple and complex route modules

backend/routes/booking.py

@@ -377,3 +377,7 @@ async def admin_cancel_appointment(
     await db.refresh(appointment)
 
     return _to_appointment_response(appointment)  # Uses eager-loaded relationship
+
+
+# All routers from this module for easy registration
+routers = [router, appointments_router, admin_appointments_router]

backend/routes/invites.py

@@ -231,3 +231,7 @@ async def revoke_invite(
     await db.refresh(invite)
 
     return build_invite_response(invite)
+
+
+# All routers from this module for easy registration
+routers = [router, admin_router]