Audio routing is not usually handled by apps, but by the distro itself, this sounds like an Fedora/Arch problem, what Fedora spin are you using?
KDE & Plasma users
KDE is an international technology team creating user-friendly free and open source software for desktop and portable computing. KDE's software runs on GNU/Linux, BSD and other operating systems, including Windows.
Stock KDE Plasma Fedora with ffmpeg-free and the mesa drivers swapped out using RPM fusion.
I had a similar issue with Kasts (KDE's podcast app) on Arch. I had to switch to my Bluetooth headset in the settings panel every single time I paused, so I guess it's an KDE problem.
Sounds like it. Given non-KDE apps handle audio fine.
This borderline looks like a troll post.
Sound to a device is handled via the audio server, not whatever ffmpeg or a media player is doing. You are very lost.
Maybe learn that part and come back to the table with better questions.
In either case, make sure pipewire is installed along with pipewire-pulse and pipewire-alsa
Additionally, bluetooth headsets have connection mode profiles, controlled by the sound server as well.
It should be controlled by the sound server, but it isn't. They both kept using the built-in speakers and refused to use the bluetooth headphones. I tested it and it was simultaneously playing a song on Firefox through my bluetooth headphones and an mp3 on Eliza through my speakers. This seems to be just a weird issue with the built-in KDE apps.
Yes I have pipewire-pulse installed. Don't know about pipewire-alsa (my Fedora device is turned off right now).
I use the SBC-XQ bluetooth profile (the only that is stable and of decent quality on Linux).
EDIT: Booted it up again and pipewire-alsa was installed too. I also installed Elisa and Dragon Player as flatpaks and now they use my bluetooth headphones.