Yes, I think it is 2 1/2 gallons. So far it works great. There is a manifold with a check valve at each sink. The return uses the cold water line. For some reason the farthest one from the source is the fastest to get hot. Almost instant. Over $3k. Installation took about 5 hours.

You may be correct about the cost. But, at least one company, Aquamotion, makes a recirculating pump system that works with a tankless water heater.

A recirculating pump without an additional heater that holds hot water will do nothing. Think about it.

I wouldn't buy one. But, I think the Aquamotion system pumps the water at a slow pace until the tankless heater comes on, and then monitors the temperature of the water in the pipe to keep it hot. When it cools down, the pump comes on again. So, you always have hot water in the pipes in your house.

Placing the water heater near the front of the garage is largely responsible for the unecessary loss. Placing it near the kitchen or master bath would help efficacy.

Fyi; For my Iris, temperature drop from the on demand heater to the bathroom is about 10 degrees so recirculating will waste energy reheating the under ground lines

I've measured less that two gallons of water run before it is warm at the master shower. About right for brushing teeth.

Since we reclaim waste water, It's not completely wasted. I have no idea how efficient that system is.