Is there an all-in-one air-to-water heat pump solution for cooling, outside of specialised underfloor fittings ?

Boiler is packing in and so heat pump seems smart. Air to water seems the obvious choice (well the only choice really), but considering the way things are going it'd be really nice if it cooled too. However it seems to have that, it's not as simple as air-to-air, as its mechanism is to pump cold water, and if your house is just radiators, it's a bit of a dud.

So I was wondering if there's an air-to-water system that also has the option to fit "normal" AC cooling, a splitter maybe ? I have zero knowledge on these systems and it's battering my head so I'm at a "I don't even know what I don't know" point!

The big part of it is also it's just not gonna happen without the BUS grant, as we're filthy filthy poors, so a single unit is basically our only chance. If push came to shove there are actually some split systems that are fairly basic and so could be done down the line solely for cooling, just push it back another year. Would just love to hear from people who have a radiator setup they replaced with heat pump + cyclinder, and also have cooling through "typical" AC methods, and how you want about it ?

Another big issue is that where the AC/s would be is in the back yard, which is fine for me as I'm next to the wall. But getting the cooling to the front of the house, with splitters I guess in a bedroom, and a downstairs room, that seems like a very expensive undertaking! Would be incredible if we could put it in the cellar, that place is permanently 15c

Sorry for the rambling, I am so far out of my depth on this one and did try to poke around, it's just too far out of my wheelhouse.