Bathroom in an old building: Is a second radiator necessary? And if yes, electric?

Thank you for your answers! So, since the bathroom is not huge, it doesn't necessarily have to be a "wellness oasis" with 24°C. But it would be nice if it were 20°C everywhere, and not just in the front area, and it is 16°C by the toilet. We don't really have higher expectations than that.

The concerns about mold in the toilet are actually good thoughts that I hadn't considered yet, thank you!

We could also easily use a type 33 radiator under the window, that would be okay in terms of space. It is true that the towel radiator is often covered more often, but I still think the idea is not bad.

Additionally, we have the situation that a second water-bearing radiator would be connected to the one under the window, and there is only a 12mm pipe there. Would it even be possible to connect a towel radiator with about 916 watts (at 75°C) over 3.50m via a T-piece to this 12mm pipe, or would it have to be larger dimensioned?

But it would be nice if it were 20°C everywhere

Even at 20 degrees room temperature, I would already have concerns that the corners of the room cool down too much and that mold will develop over time. Therefore, I would also install a proper radiator on the toilet side.