NOTE i have test fedora and fedora boot into recovery mode but have so many issue i test ubuntu/Debian and it works so good and i have not test Open BSD server or Open suse server
NOTE TTY switching is broken when you unplug the HDMI and plug it back in it dose not switch tty i have no idea how to fix that
So i manage to get a linux server distro working on the PS4 just by modifying the Kernel config the Full config is on my github and the pre compile bzs is on my GitHub as well here the link https://github.com/TigerClips1/ps4-linux-Server
So networking work fine on server you just got to configure the distro to work with the network which is easy to find online just google it here the proof of me getting ubuntu server working on the ps4 
Now why i did this because i think the ps4 will make a good dns server or an proxy server or an plex media server etc
NOTE one thing If it show an error and ask to resume-boot ignore it until you install the server distro then run resume-boot still need to fix that