Ambient temperature water is entering the system somewhere. You'd put your heat exchanger there. The replacement for the lost heat would happen to the equilibr

Ambient temperature water is entering the system somewhere. You'd put your heat exchanger there. The replacement for the lost heat would happen to the equilibriated water and could happen with a heat pump. In principle (if your heat pump and exchanger is perfect) this generates no entropy so is more efficient than putting things with finite temperature delta in contact. In practise it's probably just simpler and requires a smaller heat pump. Whether you use the waste water (which will still be a degree or two above as exchangers aren't perfect) or whatever your normal source is (ground source may be warmer) would be about cost and making the heat pump work for not-the-shower too.