"Not your AirPods" (but they are!)

So, I experience an issue that makes my anger-meter go to infinity!

All my AirPods (normal, Pro and Max) now refuses to properly connect to my iPhone 12 or iPad Pro (newest gen).

If I open the case outside of NFC range they won't connect at all and will not show up in the bluetooth device list. (the Max just makes the "thud" sound if I press any button).

Inside of NFC range I usually get the "not you AirPods - press the button on the case to share sound temporarily". If I still connect it, the connection is temporary and they will show up as a shared device in the bluetooth menu.

However if I hold the case-button for 10-15 seconds it blinks amber, and then I can connect the AirPods "normally" without the "not your AirPods"-message, and they show up in the bluetooth-menu like any other device. They are however often named "(My Name) AirPods - Find my"... But other times they have the name I gave them (without the "Find my" suffix.... I can then use them normally (most of the time), but the next time I want to use them I start all over again with the "not your AirPods" message.

I have tried to manually remove them from the bluetooth menu (and gotten and approved the message that "this will also remove the device from all your other iCloud connected devices", but the problem persists when I reconnect them.

Another weird issue is that the devices will often disconnect when they get in our out of range of my other devices (I'm not sure which, but either the iPad, my iMac or my other AirPods devices)... The issue manifests itself like this:

I connect the AirPods to my phone, put my phone and the case in my pocket and walks out my front door. When I'm 5-10 meters from my door the AirPods disconnects from my phone (which is still in my pocket!!), and I have to put them into the case to be able to reconnect it to the phone. If I then go for a walk and return to my house and walk past it, they will immediately disconnect again(!!).... Arg!

I also often get the "somebody's AirPods have been following you around" message frequently...

To summarise, the problem affects all my three pairs of AirPods, both my iPhone and my iPad, and isn't alleviated by restarting the devices, reconnecting them or even manually removing them from my iCloud account and then reconnecting them again....

Any and all help would be greatly appreciated! :)