is it mainly to feel nice on your feet or can it be used to heat the room?
It is used to heat the room. How it feels depends on how well the building is insulated.
If it is well insulated, then the underfloor heating only has to heat a little bit, so it will feel barely warm. Still better than cold tile, but not by much. If the building is badly insulated, the underfloor heating will have to work at a higher temperature to heat the room, so it will feel warmer. It's pleasant, but it's a sign you're wasting money.
I installed hydronic underfloor heating in the house. It's well insulated, so in the living room, the floor doesn't feel warm, just "less cold". I put more pipe in the bathroom and adjusted the flow so the bathroom floor does feel warmer. Of course it only feels warmer when the heating actually runs... which only happens when it's pretty cold outside and not sunny.
I set a different temperature for the day and night, so the heating system tends to wake up about an hour before I do, and the bathroom is warm in the morning.
I wouldn't recommend installing a hydronic system in your bathroom. First, because you need to run pipes and put a slab around them, which is quite a lot of effort, and it will raise your floor, adding an annoying step. Second, hydronic needs low temperature water, 25-30°C, so if your radiators run on higher temperature like 50°C, you need a mixing valve, a circulator, something to control it... It's a big mess for just one room.
If you want to install electric underfloor heating:
It's better to put some insulation under it so the heat goes where you want (ie, up). If your floor is already insulated, no problem. It's better to use tile because that transmits heat better, but that's the standard for bathrooms so no problem. And unlike a hydronic system which has quite a lot of mass due to the slab, the electric ones are quite thin, so it should heat quicker. It should be possible to put a timer on it to start it a little bit before the morning shower, so you find the floor pleasantly warm.
Unlike a radiator, it won't warm your towel though.