EmuNations

Spine

Check here to access GitHub

Spine's Wine-like PS4 emulator for Linux ONLY is capable of playing some basic commercial games, albert with usual early in development limited performance and accuracy. That said, Flatpak instructions is available on Github or you can download latest release from here (dated 01/09/2021). 

It's still very actively developed and seems promising.

PS4Delta

Check here to access GitHub

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. 

GPCS4

Check here to access GitHub

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.

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Check roadmap here

Orbital

Check here to access GitHub

The current state of Orbital at booting decrypted kernels: both PS4 4.55 and PS4 5.00 have been tested.

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Check roadmap here