I am not familiar with that exact heting system but we have hot water heat and I will never go back to forced air it is a really nice consistant heat no dust no vents to have cleaned.

See some info in this link

Hydro Air

If I understand correctly, this is akin to a heat pump Air to Air or Ground to Air system, using water instead of a refrigerant to "transmit" heat. For heating, the water is heated by a boiler, routed in a pipe to an air handler, through which passes ducted interior air to be warmed. I guess there would be a second air handler connected to an outdoor AC compressor to which cooled refrigerant would be piped to produce AC. I'm not sure what the advantage is of having an air handler instead of a furnace.

I'm sure the contractor can explain what they have in mind.

This is something to consider, and now the mini-split systems can be ducted with no wall cartridge to interrupt your decor. If you can install solar to heat the water for radiant floor heating, there may be some financial or tax advantages. Check it out carefully though. Lots of scammers are trying to take advantage as renewables are being pushed so hard.

Heating water with electricity can take a lot of electricity. All electric houses in my area are more commonly air to air or geothermal to air heat pumps for heating and cooling. Mini-splits are efficient air to air heat pumps and used for heating and cooling.

What you cite talks about Mini-split systems with a hot water coil. Are you in the US, where are these common?