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

I am considering renovating 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, each apartment is heated with gas-fired space heaters (each about 80 m2 (860 sq ft) of living space).

Now, in light of the current discussion, I am wondering if it makes sense and, above all, works to install a split air conditioning system for heating in each unit to replace the gas heating (covering rooms plus hallway). My idea is to use infrared heating for the bathroom and kitchen. Hot water would be provided by standard boilers.

Does anyone have experience with this or any opinions?

Yes, it works. It just needs to be properly planned. Large housing associations do it this way as well.