I think the usual way these are installed is they go in the basement with the drain portion going between the sewers and the house’s various drains and the fresh water portion going before the water heater to pre-heat the ground-temperature water before it enters the tank (although the DOE’s diagram indicates it pre-heats all fresh water entering the house, thereby also warming the cold water, which is probably great for showering, but not when getting a glass of cold water while the dishwasher or clothes washer are running)
This is very much a thing! Here’s a DOE explainer page and here’s a Home Depot listing
I think the usual way these are installed is they go in the basement with the drain portion going between the sewers and the house’s various drains and the fresh water portion going before the water heater to pre-heat the ground-temperature water before it enters the tank (although the DOE’s diagram indicates it pre-heats all fresh water entering the house, thereby also warming the cold water, which is probably great for showering, but not when getting a glass of cold water while the dishwasher or clothes washer are running)