I didn't do this personally, but I know rather well how account system works. What you're pretty much doing is removing an auth method from the new account and adding to old.
from:
old account A + Apple ID
new account B + PSN ID
to:
old account A + Apple ID + PSN ID
new account B
After this any progress and items you had on this account B will not be accessible on PlayStation, but Playstation will use progress and items on account A
To do this you first need to login on Epic website into the new account B using PSN. At this point you may be asked to add email, name and password for this account. Then you'll need to remove PSN connection to this account.
Then you need to login into your old account A on the website using Apple ID and add PSN connection. After that your Playstation will use old account.
If you'll be asked to provide an email for the old account, at least for gmail you can create aliases, e.g. if your email is email [at] gmail [dot] com, you can do email+any_text [at] gmail [dot] com and it will still go to your email [at] gmail [dot] com.