On PC you'll be able to access Forsaken, as well as Shadowkeep if you bought it there. Your PS4 characters will reap the benefits of that content and items. However, of you return to PS4 with your characters via cross save you will not have access to some Forsaken activities (a lot is being included in New Light). DLC is basically bound to the platform you purchase it on, so you need to purchase it on all platforms you want to play it on. Stuff you earn, though, will travel with your characters between platforms unrestricted.