I know what you're talking about, my condolences.
I had that bug too at times, and AFAIK it isn't even Linux-specific; unfortunately, fixing it requires praying to all the gods you know of and hoping one of them hears your plight.
Here are some of the forbidden rituals I've had some success with:
- Whatever Proton version you're using, change it (or change it back if it's the second time you get this problem);
- Rename or delete the HD2 compatdata directory, something like ~/.local/share/steam/steamapps/compatdata/six_digit_number_idr;
- Restart your router if your ISP gives you a different IPv4 address every time (SoL if it doesn't);
- Disable IPv6 on your system;
- Use Google's DNS servers;
- Use non-Google DNS servers;
- Delete nProtect (it should be downloaded and installed back again automatically).
If none of those work, which wouldn't surprise me, I fear only time will fix your game as it did mine.
As for the anti-cheat being the cause: I don't doubt for a second that it makes the netcode janky as fuck, but I have ~600 hours on record, and not more than 2 hours were on Windows 10. Linux's fine.