The last drivers to support the P4 will be the 580-series drivers, so anything in that vein (580.190.04 seems to be the Very Latest of them on the Linux/Unix datacenter side?)
Regardless of open vs proprietary module source, it was NVIDIA who deprecated and then cut off the Pascal/Volta cards in the 590 driver line as @DjP-iX points out - they will not work even with the proprietary kmod compiled.
I have a couple of P4s that were impacted by this, so I share your frustration, especially since the T4 is still significantly more expensive for a home user wanting a number of supported CUDA cores.