This is now the second Shadowkeep quest which doesn't get marked as a complete. Happened with a previous quest, too. Can't recall what the name of that was.
Having done the 'Beyond' quest now 3 times, collected the artifact 3 times, used the full armor set (if that makes any difference)?. Always end up back to the orbit, and I can see that the campaign is still available on map.
Would like to use this opportunity to also say that I'm soon used more Googling around about how to play this expansion, rather than actually playing it. [b]This expansion is just absolutely awful.[/b]
Last week, In the Deep was the Weekly Repeatable Mission. This week, it's Beyond. It's intended that it's repeatable.
When you're trying to do Beyond for the Shadowkeep campaign Quest, please go to the location while on Patrol and interact with the Mission start point. Going to the activity directly from the Director loads you into the repeatable version of the mission (which doesn't grant you the item at the end or give you the full cutscene).