FWIW, I've had no issues here with my Lenovo ThinkPad Z13 and Fedora 39 (Bazzite).I use my 8BitDo Ultimate Bluetooth controller almost daily as well as my Sony WH1000-XM5 headphones, both work just fine.
I'm on BlueZ v5.72 and kernel v6.6.14
What distro / kernel / BlueZ are you on? If you're not on the latest BlueZ and/or a recent kernel, you should update them.