AirPods won’t connect to another device when paired with one

Hello,

I recently bought some AirPods Pro 2nd generation that I was going to use with an iPad Air and an iPhone 12 Pro, but I'm pulling my hair out over a pairing problem.

When I pair my AirPods to the iPhone, everything works perfectly, the iPhone sound comes out in the earphones. But when I then try to switch to hear the sound of the iPad (which should be possible, since both devices are registered with the same Apple ID), I can't connect the earphones to the iPad - it just keeps spinning endlessly in the audio devices list... Same thing if I pair the earphones to my iPad, everything works fine on my iPad, but I can't connect the earphones to my iPhone.

Any ideas? Thanks in advance !