Fyi for anyone who hasn't played CS:GO in the last couple of years, CS:GO now has the option for short competitive matches which are Bo16 instead of Bo30. I'm not sure they're quite down to "20-minute firefight"s that OP asked about, but they are definitely much easier to get into than traditional competitive matches.
My go-tos are tf2 and tf2 - that is Team Fortress 2 and Titanfall 2. Both work great on Linux and have really dedicated communities. Titanfall 2 even has the Northstar client.
Not sure if you're fine with a paid game, but Halo: The Master Chief Collection recently got Linux support for multiplayer - though they have the Steam launch options reversed so you have to select EAC disabled at launch, in order for it to be enabled lol (thus allowing you to play online)
Additionally, Halo Infinite's multiplayer mode is free, and also works on Linux.
Some EAC games support linux like halo. I played MCC and the performance was fine, but I found the game to be unstable when interacting with the menu/UI.