PS4Delta is a very high level PlayStation 4 emulator, written in c++. It's quite early in the development stage and barely manages to initialize all firmware modules though is actively being worked on.
1 commercial game running, though not playable with very low FPS since there's no optimizations at all currently. GPCS4 recompiles all shaders, untiling all textures and upload all buffers every frame, making it quite inefficient.
The current state of the Wine-like emulator for Linux is unknown since it's closed-sourced. That said, the only available artifact is a demo version which is a Flatpak package. Don't expect much from this demo as it is a proof-of-concept.