Even if you could, I wouldn't advise doing this. It says to Sony "I have trophies for digital games I didn't pay for." And you know what that means. Assuming they can tell whether or not a trophy was earned through a physical copy or a digital copy on the backend.
But this argument isnt the reason for..
If u share your games with a friend or a family member => u can login on their console and set it as your primary console (you can only set one at a time - but you change it easily even without acces to the console (Sony Website Login...)) => then they can download "your" games and can play it with their own account (even offline) => but if you want to play with your account on your console you have to be online. So you can have Trophys for digital games even if u dont own them on your account
blabla => my wife plays a lot of my bought games on her playstation even without owning them and trophy sync is no problem at all.
so we always buy a game 1 time for us both and we can play it online together if wanted(PS4, PS5)
I woudnt recommend to sync trophys from a jailbroken playstion too for sure. Even if u update your console afterwards to do it - there is still a chance that the server can detect like the goldhen folder which is created automatically on your hdd when u used goldhen, then their is the apphistory some other files, savegames from fake pkgs and some other shit. (its only speculation but its very risky...
I got my ps3 banned years ago after using a jailbreak "stick" for a long time => updated => banned like 3 hrs later after i went online (Hardware Ban and Account Ban...) my bad was that i only updated the console and not to do a full restore in the recovery mode.. (but in that case all files would have been removed..)
there was like a theory to do a backup of your current console to a hdd and restore it on a non jailbreaked one but this wouldnt work cause u cant restore the trophys from the backup hdd...
and synced Trophys from Fake PKG Games could be a risk too (dont know it for sure - so thats only speculation too..)
its not like the ps3 era where u could cheat trophys and sync them if u did it right... and i saw a ps4 trophy unlocker which should work on your jailbreak ps4 but to sync these nowdays would be super stupid.. would be super sus if u unlock all trophys in like 1minute or even all in the same time... this would be easily detectable
maybe it will work after updating it to newest firmware.. => but u will have to link your local account to your real psn id (or a new one) afterwards to sync the locally stored trophys and i woudnt do it
even if u got the trophys synced and the account isnt banned.. you may risk a hardware ban which means u cant go online anymore with it.. and with a updated ps4 u wont be able to jailbreak it again..
Edit: someone claimed it to be done with a SYSCON Glitch but that isnt easy at all. Required a lot of hardware skills, soldering etc.
