Install electric underfloor heating in the bathroom?

There are special valves for the return flow that only allow a certain amount through the [fb] pipe. Many skip these valves and connect the return flow directly, then you have the described problem. When the valves are installed, you can set the temperature that the tiles should receive. It is much more economical than electric and controllable (valve costs under €100). The whole thing is called an RTL valve.

The electric version is great when the screed is in place. It is just a makeshift solution.

If the screed is still missing, definitely install underfloor heating and not some retrofitted thing. You don’t buy a new car with your own configuration only to immediately add new custom extras after the purchase.

Electric heaters are expensive to maintain! You heat there at three times the cost of a "normal" heater, and in the bathroom, where they are often operated continuously, I wouldn't do something like that if I had an alternative. The low initial costs quickly pay off badly. It only makes sense during renovation measures when underfloor heating is no longer possible AND when there is also a radiator present that can take over most of the heating capacity.