I was thinking about trying to build one a while back. Lineage OS is probably the best candidate. It is free, open-source and can run on x86. I never got around to attempting the build tho cuz while it feels possible it would be much more work than I want to put into this hobby.
First I assume some major work would go into tweaking it to run on x86-64 then would have to build/add the ps4 drivers.