Online: How to tell what quest

I wish there was a better way to see what quest is currently being played. In the lobby it says the story quest but not the current quest right?

I hate getting into a match to have it at the end of the quest and mess up my personal save. Do I not understand how it works? I’m on PS4. Thanks.

In Online Matchmaking list, you only can see the latest Story Mission the host is currently at.

However, you can check which side mission he’s doing at the moment in the hub menu, mission list. Of course, you have to enter the game first before doing so.