Apex legends works on Linux (Wine + DXVK)!
Just so that all the the fellow Linux gamers know, I got a Apex Legends running on my machine with very good performance (RTX 2080 / i7-9700k, running Ubuntu). Played a few games online tonight without any major problems.
The only thing that didn't work is the Origin overlay, trying to open it would crash the game. However, you can join your friends party through the friends tab in the game, so the overlay isn't needed. (Also, ask your friends NOT to invite you, as the origin invite will get stuck to your screen, just join manually.)
I used the Lutris install script for Battlefield V, which sets up origin and DXVK. Then in Origin I just installed Apex Legends instead of Battlefield.