Heat the hobby room in the basement with infrared or electric heating?

The two who recommend a separate heating system say that underfloor heating is too expensive.

We retrofitted an underfloor heating system for a basement room (40m²). Including an additional manifold and all work, it cost us 1350€ net extra. We had the radiator valves installed so that we can switch it on only as needed.

ok, yes it wouldn't be that expensive either, but still more than twice as expensive as the radiator. Maybe I should ask what the additional cost for a [floor heating] would actually be and with which option I could heat faster.

I would recommend infrared wall panels to you. This way, you have direct radiant heat as soon as you turn them on. I have two of them hanging on the wall in my hobby room (22 sqm) in the basement. One with 600W and one with 1000W. The things are mounted on two opposite walls. The couch is located (almost) exactly in the middle.

Such infrared wall heaters are available in many variants (cheap in white) or also expensive with stone slabs or some kind of decor.

It is after all a hobby room that you do not want to heat continuously, but individually and also temporarily depending on need and feeling. This is precisely the prime example for an infrared heater. For example, we will heat our entire house this way; underfloor heating alone seems unsuitable to me there because of its inertia. If you look around a bit, you will also find stylish and high-quality devices, whether as modules on the ceiling (optimal), on the wall, or stylish mobile solutions. Even heating paint would be a good option, but for a hobby room I would definitely use a "normal" infrared heating module. On request, you can also simply plug the basic version into the socket and have zero conversion costs for the hobby room; in addition, all of this is also widely available second-hand.