Bluetooth keyboard stops working on iPad (but not on external display) after going to sleep

Hello,

Since today, there is a strange thing happening to my set up.

I have an iPad connected to an external monitor using Stage Manager. To control it, i use an old iMac BT keyboard and a Magic Trackpad.

Since today, after the iPad going to sleep, randomly my keyboard is not able to type anything in text fields on the iPad ONLY. Yes, if i type something in an app on the external display, it works. If i put the pointer on the iPad and switch app with the keyboard, it works. But impossible to type anything.

Nothing is able to make it works again, except restarting the iPad.

Is this a known bug ? I haven't found anything.

Thanks