Thanks for the feedback.
I will keep my Delta status card on my phone easily accessible then (I don't have a physical card, I have the status from a challenge and from my understanding, they don't issue the card).

From my experience with SkyPriority, I usually show my ticket where it's clearly written Skyprority to pass fast line security, priority boarding, etc.
In this case, I don't think this will be written on the ticket.
Do you think it's ok to show the Delta status card only? I'm not sure the agents are all very clear with that... Should I be able to ask during checkin to put skypriority on the ticket?