Tire pressure warning and other issues

Several things could be happening here. The tire pressure warning is related to the low pressure in your front right tire. Since you're experiencing other issues along with this, it points to something more than just simple deflation. The ABS light, vibrating steering wheel, and loss of power steering could indicate a faulty wheel speed sensor. The ABS uses these sensors to detect if a wheel is spinning at a different rate than the others. This could be triggered by the low tire pressure. Have you checked the tire itself for any punctures

Puncture is what I feared. I had a look, but couldn't spot anything obvious, like a nail or screw. I'm not really sure what a wheel speed sensor does. It sounds complicated, but could this really all be linked to just the tire And if so, how does a dodgy tire make my power steering go bonkers

It's likely all stemming from that tire issue. A significantly underinflated tire changes the rolling diameter of the wheel. Your car's computer sees this difference in wheel speed through the wheel speed sensor, which can mess with the ABS, stability control, and even the power steering assist. If you cannot visually identify damage causing the loss of tire pressure, it is very possible that a valve is defective. I would recommend taking the car to a workshop to have the tire and valve properly inspected. They have the tools to do that.

I took it to the shop, and you were spot on. Turns out the valve in the tire was defective. They replaced it, checked for leaks, and everything seems back to normal. Cost me about 280€, but at least it's fixed. I learned something about wheel speed sensors too