On the PS4 I'm currently in the middle of the Beyond light campaign. But I wanted to pick up some stuff from Spider and now It says when I hover over it to start the "Last Call" campaign mission again. Obviously I have no interest to do it all again. So I had to bypass it by going with a friend who doesn't have the bug to acces it. Please fix this or tell me how to.
Found the fix, for anyone still looking.
Go to the tower, on the left of the Postmaster is the quest kiosk. Access the kiosk and select the bottom right option on the menu. This contains the starting mission of the questline, select it and it will remove the quest inventory full error. You can now play the mission.
Credit to Reddit user Natandty for finding this fix:
https://www.reddit.com/r/DestinyTheGame/comments/kdaryj/quest_inventory_full_cant_do_first_mission_on/gfxw6hf?utm_medium=android_app&utm_source=share&context=3