In API 581, for non-flammable and non-toxic consequence, it only mentioned 2 main types and they are steam leak and caustic/acid leak. It did not mention anything about water leak in this case. Does that mean I can’t perform Level 1 consequence analysis for equipment with water as service medium?

Yes, you can because water is representative fluid and you can perform Level 1 at least. There are other questions such as "What consequence do you expect?"