Install the games on the new console as you did with the old one. You can use Checkpoint to restore your savegames on the new console if you want to.
And even though if you could do a "system transfer", you'd have to install the games again on the previous console. There is no point.
only ps5 updated to latest firmware can go on psn, jailbroken ones just don't use psn or they risk getting flagged or banned, altho spouting profanity in online play alredy does that