Stored payments just shows me that I have an AMEX saved. It doesn't give me any info about what kind of card it is. The method Gooselee described shows Delta skymiles card member, the level, and a picture/icon of the card. I think it's easier to find in the app, and in the app it is actually a hyperlink to stored payments.

Since OP upgraded from gold/plat, I think his profile might not show the change to reserve until the billing cycle closes and his cc RDM post.