No. To play online, you need official game files and a valid PSN license. PKG backups are for offline only.
However, I can offer a legitimate guide to obtaining and installing Black Ops 3 on a PS4 (or PS5 via backward compatibility) legally: call of duty black ops 3 ps4 pkg link
Most users interact with these files indirectly when downloading games or DLC, such as the Zombies Chronicles expansion, from the official PlayStation Store . No. To play online
: Navigate to the PlayStation Store from your console's home screen. such as the Zombies Chronicles expansion