They do indeed, same with heat pump style water heaters used in America.

Can you link a drop-in heat pump replacement for my Vaillant gas boiler mounted in tiny apartment bathroom, which heats the radiators in the winter but also provides hot water year-round?

Yes. For example Daikin Altherma, but I'm sure that every brand has a compatible system

It seems like it requires an external unit. I cannot easily mount an external unit. The bathroom is far from external walls, boiler is connected to the shared air intake in the wall that leads to the roof. So this doesn't look like a drop-in replacement.

Outdoor units are pretty flexible in the sorts of places they can be mounted and the insulated refrigerant lines can be run to the interior of buildings fairly easily. Don't just assume a solution can't work until an expert says no.

And even if you can't hook into your existing radiators wall mounted mini splits don't require extensive interior changes to function (plus you get cooling as well)

I do have a mini-split AC which can also provide heat. It is OK for autumn and spring but it is a no match for a radiator heating when it's really cold outside in the winter. Yes, of course I can run the lines through the whole apartment but this is a much costlier proposition.

Talk to your local gas/water/heating instalation company, they are the experts.