I have to wonder if it's possible to ever even guarantee something that can't be trivially bypassed on Linux - Windows, sure, it's possible with DMA, but it's damn hard. On Linux you could just compile a spoofed kernel or a DKMS module or something.
On Windows you can't do this, so you have to go through one of the known APIs that anti cheat software monitors or find exploits in kernel drivers to get in and poke at the game's address space. They also look for known vulnerable kernel drivers on boot and block loading the game if they find them.
Some anti cheats run on Linux, but they're borderline useless and trivial to bypass.
Unfortunately for anti cheat software to ever work on Linux would require signed and attested kernels and locked down OS software. Something that will never fly in the Linux ecosystem.
Locking down Linux totally is impossible, but the same very obviously goes for Windows and even macOS as well. Locking down a Linux runtime well enough to play online games seems trivial in my opinion. It's just a lot of work that would be better-spent preventing Windows hackers from pants-on-head insane DMA exploits.
Or deliver the game as a container format, like snap or appimage to bypass most of the system.
Or demand the installation of a kernel driver like they do on windows.
or just give up on kernel level aticheat since they're been breached all the same, just as windows are restricting their power too.
easy-anticheat has a linux version. Developers have to disable the support intentionally.