Which version of Bazzite are you on? Bluetooth has been having connectivity problems in the latest versions (a regression from the Bluez driver upstream, I believe).
I rebased my Steam Deck to 39-20240328, and everything seems to be working as expected. 39-20240414 might also be okay, but I haven't tested it myself.
ETA: I haven't been able to connect my primary BT headphones to my Deck, but my Steam Controller and a different pair of BT headphones are fine. Might be a similar case with you; I don't know why one works but the other doesn't.