Do you read French?
Apparently you can get Manjaro for the PS4. I assume it’s French based on the URL.
Do you need to be able to run homebrew to install it? Or can you dd the image to the hard drive, and it’ll boot? Probably need homebrew access. That may or may not happen. Depends if they decide to release the exploit for newer firmware.
Yup, you need a PS4 Linux Loader.