Apex is listed as Steam Deck Verified. Since Steam Deck and desktop linux use the same compatibility tool, Proton, that means both should be supported.
Additionally, the last time this happened, Apex unbanned all of the desktop linux users, which is at least a soft-confirmation that it's supported.
edit: as per requested; There is far more to any system than just the OS or a single piece of software. Simply because both systems use the same core, the OS isn't a copy and paste. Additionally, the varied components result in very different results. tldr; Linux != steam OS despite being built on the same core.
“Unsupported” (or “your mileage may vary” as you put it) means it lacks support. As in, if you try to contact support they are totally in their right to answer “sorry, this platform is unsupported, you’re on your own” if something doesn’t work or is buggy.
“Unsupported” does not mean that it’s a bannable offense.
Given that, let me ask you: why do you think trying to run software on an unsupported platform without malicious intent should be banned, as you seem to imply?