Multi-split air conditioning system for 100-year-old historic building for heating

I am considering the renovation of a multi-family house that is about 100 years old and has 5 residential units.

The building has not been renovated (no thermal insulation, double-glazed windows). Currently, heating is provided by gas heaters in each apartment (each approx. 80 m2 living space).

Now, in the context of the current discussion, I am considering whether it makes sense and especially works to use a split air conditioning unit for heating in each residential unit as a replacement for the gas heating (rooms plus hallway). My idea is to heat the bathroom/kitchen with infrared heaters. Hot water would be provided by standard boilers.

Does anyone have experience or do you have an opinion on this?

Yes, it works. It just needs to be planned accordingly. A large housing company does it the same way.