If I'm understanding this correctly this opens up the door to a serious type of rootkit.
It's not a matter of attackers having access to the data. It's that they have replaced your hardware with malicious hardware.
Additionally It can be trivial to gain administrative capacity on a personal computer. But in a regular case you can just reinstall the operating system. This would survive that.
It's important not to use a mechanical drive for modern gaming (if you are). Modern games can expect to be able to load assets more or less immediately upon request, otherwise your experience and performance suffers.
Your cpu is below the minimum requirements for windows 11 which may cause you challenges in the near future. But if you're comfortable with Linux that's largely mitigated.
Disabling CSM (in your bios) and confirming your operating systems are configured for uefi is important.
Enable "above 4G decoding" in your bios.
Confirm your bios is up to date and that your ram profile is configured correctly. (Lookup xmp/docp)
I believe your platform is too old for the Intel arc b580 but I suggest researching that option as it fits your budget. Otherwise a 10GB or higher GPU if you can find one. (Probably need to search the used market for something like a Radeon 6800 or better)
The closest match that comes to mind would let your players bank the time they don't use. Using an n+5 configuration. The software cutechess may be capable of it but it's not online.
But what bugs me is it would be a goofy way to play as different positions can demand more thought than others.
You would probably need to make your own custom rule set and host it yourself or do a regular game on something like lichess and enforce the time constraints outside of the platform.
Was it by chance something by Rooster Teeth?