That's annoying. Honestly it sounds like your IT dept is missing some expertise, and maybe tried to be too clever by installing some hacky add-ons, which destabilized things. It seems like something of a ridiculous stretch on their part, for example, to think that Jack would be required for bluetooth.
That said, as long as they're willing to be hacky: bluetooth audio worked reasonably well for me _until_ I got a headset with its own dongle. At that point the original bluetooth dongle stopped pairing reliably with the speakers I was using. That prompted me to switch to pipewire and it's been rock solid since. You might suggest to IT that they experiment with pipewire (since it's the new hotness, they may actually take you up on it.)
Jack is apparently needed to get Bluetooth to emit audio reliably... but I would not put much trust in that since it didn't fix Bluetooth not working.