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.
~~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.
Are you using the dongle that came with the controller? Bluetooth via direct connection doesn’t work for these controllers, you have to use the dongle. The Bluetooth direct (no dongle) only works for mobile devices.
Give Spiritfarer a shot, full controller support and even a bit of harvest, fishing, and adventure to boot. 30 hours easy if you take your time, more if you want. Super chill game.