Heating in the kitchen "necessary"?

That is a good question
She simply doesn't want any. She thinks it would be too expensive, makes too much mess, too complicated, and wouldn't be so "healthy" if you get older and have any problems.
I generally don't believe it would be much more expensive than replacing all the radiators etc., but well, what can you do?!? She doesn't want to and with that the topic is (unfortunately) more or less settled.

Don't you think you can convince her with enough persistence? We can gladly help you refute her arguments. I can't tell you anything about the price, but you can get a cost estimate for the milling. They only need a floor plan. The big advantage is that you no longer need radiators and can place furniture freely.

It was not about reducing the heating demand, but simply about whether a heater is absolutely necessary in this room at all

That's basically the same, as I specifically referred only to the heating demand for this room after all.

and it wouldn't be so "healthy" if you get older and have some problems.

Precisely with old age ailments, underfloor heating is said to be perceived as pleasant, and among female friends there are surely households where experience has already been gained with it. I also know underfloor heating from such friends, where I visit quite often throughout the year, I have none myself, and thus the comparison: the difference would not be dramatic enough for me to be definitely for or against it. In a new build I would find underfloor heating more contemporary, but in a prefabricated house from 1978, it would not measurably change the market value even if well renovated – again, to the extent that it neither acts pro nor contra.

So at the moment we have no heating in the kitchen of the rental apartment (there is one, but we have blocked it off to somehow fit all the electrical appliances and storage in this difficult room). Unfortunately, there is also no heating in the hallway in front of it. The door to the living room is taken off, so the radiator there heats both the hallway and the kitchen (although the doors to the other heated rooms are often open as well). It is always terribly cold in the kitchen in the morning. In the meantime, we have hung a thick wool blanket in the door frame (we unfortunately had to take the door off there as well due to lack of space), which we either place on top of the cabinet or let hang down... depending on whether we want the heat to come in or stay inside. If the oven was still on late in the evening and the blanket was hanging down, it is somewhat okay in the morning. But honestly, if there is not a radiator right next to/in front of the kitchen, I would definitely plan for a heater in the kitchen!

I think we are also drifting a bit off topic

One does not go without the other. You are making a concept where the purpose should be considered. For example, I notice that an open door is mentioned, as well as a dining table placed centrally to the door.

Because I would basically leave the concept so that when you go out of the door, you place the dining table fairly centrally.

That is poorly thought out: the door is in the way if you want to walk around the table, and if you are sitting at it. If you put it into the kitchen, you cannot carry the food out without being in your own way.
It is much better to plan a door where it does not disturb. Ideally always facing a room corner rather than centrally. Also because of the possibilities for placing furniture.

it is so important that the refrigerator is in close proximity to the refrigerator.

It is simply impractical to have to take some things out without a surface nearby. The fridge door must consequently stay open a bit longer.

And then comes your issue of the lack of space.
Infrared would probably only be a nice additional option.

That is a good question
She simply does not want one. Says it would be too expensive, makes too much mess, too complicated and would also not be so "healthy" when you get older and have some problems.

Although I consider a radiator in the kitchen very, very practical, you should not assume the 1970s underfloor heating standard, but today’s technology. Because that is what the fear of health problems is based on: ignorance.

In kitchen planning, is almost perfect. The mistake or the best always lies in the details.

Over the weekend, the current tenants will move out and I will go with a friend who is a heating engineer to take a look at the whole thing. I will probably plan for a heating system, but I think it will probably be a heater in the baseboard, even though it is not that efficient. In my opinion, however, it is probably sufficient to provide warmth. : Let's put it this way, the table should not be placed directly in front of the door, there is still enough space to walk "around it." My sister has a similar layout, I think it's all fine that way. We also have to adapt a little to the current circumstances. I will be in the house from next week, then I will think about it again and take another look at it calmly.