~~TBH I am not using Linux and am using a Pro 2 like OP, however I was attempting to connect to my laptop (Win 10) via Bluetooth only, and it wouldn’t work.
That’s when I discovered Bluetooth to Bluetooth only works with mobile, and to connect to a PC you have to have the USB dongle that came with it. If OP is saying it works fine direct connection I’m recommending they try the dongle.~~
EDIT: I am using the Ultimate 2, not the Pro2, this may not apply. I apologize.
If it’s the Pro2 the dongle should be in the charging base under a little flap. When I get home I can take a pic if needed. To be clear: I am not running Linux but I had this issue attempting to use the controller Bluetooth without using the dongle.
EDIT: I am using the Ultimate 2, not the Pro2, this may not apply. I apologize.