When it is a third party log-in, you assume you have shared saves on whatever system you have the game.
It's like playing FF14 on the PS4, I would assume I can log into my account on my PC and play the same characters.
In the case of Fortnite, you can do that. You can log into the same account on PC, Mobile and PS4.
OR you can log into the same account on your Switch, Xbox One, Mobile and PC
Though as soon as you log into a console, its locked into that crossplay family forever, without warning. There are lots of PC players that logged into the PS4 once just to unlock a quick free skin. Many are calling it Sony's Trojan horse. They offer a free skin, and as soon as you grab it, you are now locked out of ever logging into an Xbox or Switch with that account now.
Did Sony advertise the exclusive skin? If there was no warning accounts were about to get abducted, this whole debacle just keeps getting worse.