Hello eveyone here is the un intellegent Penguin here

IT is not a double check valve
the actual term is reduced back pressure assembly (RPBA)
the main difference is the air gap between check valves when water is dripping or pouring out the air gap in the middle where the basket is you have a problem - a check not sealing to be precise. this indicates that the valve req service and testing to meet city codes - its been a few years since I have done back flow training though and I'm a little fuzzy.

the double check valve is similar except it does not have the air gap and drain in the middle of the bottom
the other is a trap primer as previously stated

the rpba is there to protect the city water from contaminants. likely as since the water heater is used for heat the inspector called for it to be installed (rob said they use the heater to heat water for a fan coil?)

Good day every one and happy inspecting