I'll be surprised if they still build out-of-the-box with a newer kernel and compiler.
I wasn't wrong: 390.157 driver no longer works with kernel 6.5+ - Linux - NVIDIA Developer Forums
Amazingly, for this exact driver, someone has patched it to keep it working, and its available on a PPA which might make things easy for you: nvidiaexp : Daniel Letzeisen - although I suspect results may vary.
In any case, I'm adding this to my list of reasons why I'm on my last NVIDIA card (my other main reason being this 15 month-old, widely-experienced problem: External monitor freezes when using dedicated GPU - Linux - NVIDIA Developer Forums).