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.
I hope you understand that you're getting downvoted because your reply is very low-effort that refuses to go into any detail. Therefore, it comes across as malicious, arrogant, and dismissive.
You're pretty misinformed here. EA (or rather the internal studio, Respawn) had to include the EasyAnticheat .so file (which is specifically designed to allow EasyAnticheat to function under Linux -- .so files are the Linux equivalent of Windows .dlls) in their Apex Legends builds to begin with. Otherwise, EAC will not run on Linux, period. This developer opted-in to EasyAnticheat running, and has continued to opt-in to this.
This isn't Valve "tacking on" support, the presence of that file is an explicit "we're permitting this to work" (even if they don't "officially" consider it supported).
A closer analogy might be selling uncooked food that is safe for people with a peanut allergy and then one day adding peanuts as an ingredient after they've paid for a shipment. [It should go without saying avoiding a peanut allergy reaction is more important than preventing a company locking you out of entertainment software you paid for]
It's my hope that corporations will learn it's a dumb choice to needlessly cut off their Linux users but a better choice would be to not play video games where a company can arbitrarily lock you out in the first place. I hope someone is working on a libre version of Apex.