The great thing about heat pumps is you can run them in reverse to become an AC, only requirement is a drain for the condensate.
Although you could pipe cool water through the radiators, it's an ineffective form of cooling compared to blown-air systems, and retro-fitting a blown-air system is much more costly than a heating-only heat pump.
Once room and floor temperature match, condensation doesn't occur anymore as long as you keep it running.
However it will not cool like an A/C unit, only something like 5°C reduction. This can be enough to get a decent night's sleep during a summer heatwave.
While our house is relatibvely small and we kept the units (which also do heating as well) confined to the main living space, it wasn't especially burdensome. The bulk of the work was installing the behemoth of a hot water tank!
I'm currently investigating options for kitchen sinks and such. It feels quite silly to have a long length of pipe leading from a central source for a small amount of warm water to wash my hands.
There's a limit: you can fill a medium saucepan with boiling water, but large/industrial-kitchen pans will exhaust the boiling water and you'll need to wait for the next batch.
It's fine for general household use.
Daikin (and presumably others, but they're the ones we went with) do have integrated tanks/heatpump internal units. It might be worth having a think about your actual needs and it may be that there is a solution.
My experience with electric hot water taps is that they've been universally awful and only a last resort, but equally the state of the art may have moved on since I last looked!
With an AC the advantage is that the condensate is forming inside the AC when cooling the air.
From a pedantic point of view, it is quite literally the exact same as an AC. Air conditioners are literally heat pumps.
Common installations reuse the wet systems we have and are air to water, which was until recently the only thing the grants covered (and now it’s still lower for a2a).
Most importantly it's not the same in the way of me not feeling the chill. It's stupid, as I know the house is cooler than the outsides, but the actual split system delivers the cold air right to where I feel it and this thing just makes the ambient temperature down to 25c without me even noticing.
I don't want to know what it costs to install (I got it with the house), but split system costed lol nothing in eastern european dollars and took some guys less than half a day and zero permits to install too. For better or worse the heat pump doesn't live in the same locale I had that.
This is more like what they're talking about, but they do come in a lot of shapes and sizes and can be more or less integrated into central systems.
Like, sure, but the word has a specific and a general meaning, conventional use is only the specific meaning.