That scenario would definitely be the time to use SBC-XQ.

http://soundexpert.org/articles/-/blogs/audio-quality-of-sbc-xq-bluetooth-audio-codec

(I have the over the ear XM3 that don’t support multiple devices, but also have a Bose 700 that does. The Bose 700 does AAC, but I find SBC-XQ better. On the Sony it’s a toss-up, so I stick to LDAC. I’m using Fedora Silverblue 39 with PipeWire for reference.)

I’ve been on Fedora 39 since it was branched (in September), using Silverblue and GNOME. No issues; everything’s great here.

Note: You can actually play Halo on a Steam Deck. I’ve played it with friends over the internet and two of us were on a Steak Deck and Linux desktop. The other two were on Windows. It worked well.

(But, yeah, there still are a few other games that don’t have anti-cheat enabled, such as Fortnite and Destiny 2.)