Buy a house with electric heating? Or a new terraced house?

The townhouse may be larger, but one should not underestimate the factor of a detached house, even if it might be smaller in terms of area.

In our townhouse, I especially like to call the ground floor a "tube floor." All the rooms are oriented to the left and right, and you walk from front to back. This greatly restricts you in terms of room design. Our townhouse is 5m wide and about 12m long.
The room layout on the upper floors is usually better because the stairs run centrally upwards and the rooms then spread out in all directions from there. And although I am very athletic, the narrow stairs in the townhouse annoy me a lot by now.

With a detached house, you also have space all around the house; if the garden is e.g. large enough, you can build a garden shed for hobbies or, if heated, even for guests. It then appears larger, although it may not be, and you have significantly more possibilities for redesign.

Our new house is only about 40m² larger but appears about three times as big because you simply have more space in all directions.

In the end, it is your taste that counts. If you want to compare both houses on the same level, you have to factor the money you would save with the cheaper house into your calculation and see what you could do with that money. Replacing the heating costs 40k, so what will you do with the other 40k?
Always keep in mind that you are probably making a decision for the next 10-20 years or more.

Furthermore, the living area is spread over 3 floors, whereas in the existing house it is on 2.

That would already be a big point in favor of the existing house for me. Having to climb only 1 staircase instead of 2 several times a day.

and the pellet stove, which is also not very visually appealing. You probably can't have a glass stove with pellets.

You can simply replace the stove with a fireplace if you want.

What speaks against continuing to look if neither option really suits you?

Apart from that, I would also choose the new terraced house with a child (as I assume). The aspect of quietness is not as important with a child, the central location is advantageous. Possibly the resale value of the house could also be considered.

I personally do not find a narrow entrance area disturbing, but rather "normal," even if many of us dream more of an "entrance portal." ;-) A rather small kitchen-living-dining area can, in my opinion, be compensated by clever furnishing and consideration of what you really need in that area. Then it is more "cozy" than "loft-like." Both have their charms in my opinion.

I think most of it has already been said, but what still gives me a bad feeling is the following thought: If the previous owners were so stingy that they even skipped the heating, what else did they cut corners on? Where else was there "shoddy workmanship"? Repairs were certainly not carried out by professionals, etc... Normally, one approaches a house with the mindset that you build it properly and correctly once. Better to spend a bit more money for peace of mind forever. But the house seems to have been built on an absolute shoestring budget and with a very short-term perspective. Usually, you calculate this beforehand and come to the conclusion that pure electric heating + instant water heater is more expensive in the long run than a heat pump (or in 2008 probably gas). Especially if you take this into account right from the start.

I have never had an infrared heater, so I cannot judge the comfort, but I see the following advantages and disadvantages:

Advantages:
Very quickly adjustable and very fast heat availability.
Usage can be optimized strongly to what is really necessary.
Low to no maintenance costs.
Easy replacement in case of defect.

Disadvantages:
Poor efficiency 1:1 and therefore higher operating costs.
Visually, it could hang in the way or not look elegant.

If you decide on the existing building and the appearance doesn't bother you too much, I would probably keep the infrared heater.

Infrared: 40kWh/m² x 140m² + 3200kWh (hot water) = 8,800kWh per year x €0.3 = €2,640. Heat pump: 8,800kWh / 3.5 COP = 2,933kWh x €0.3 = €880 €2,640 - €880 = €1,760 40k / €1,760 = 22 years

Since the lifespan of a heat pump is 20 years, the costs are not significantly different in the long term, and there is no effort.

A photovoltaic system might be more worthwhile under certain circumstances.

That is probably the most ridiculous thing I have ever read. Professional companies never botch things and doing it yourself is always botched. It can only come from a banker who really can't do any manual work himself.