According to the game's Steam store page, it uses Easy Anti-Cheat, which generally does not work in Proton. Pretty common problem for people who want to play modern online games. I'm surprised you say it works for you.
EAC has an option for Linux/Proton support, but it has to be explicitly enabled by the developer. I believe it ships a Linux binary that runs alongside the game, poking into the wine environment. EAC works just fine in proton with Halo Infinite, for example.
It works fine, I've been playing it on Fedora since The Finals was released.
There is a specific Proton EAC runtime you might have to install. Check under Library -> Tools.
EAC works fine if the game has it enabled for Linux, which The Finals does (I play it).