In the US lounge access comes mostly from paying annual subscriptions or earning passes through spending rather than booking a specific cabin. Also, while you're chilling in the lounge people at the gate are hearing things like "Because of Regulation X this flight now requires gate inspection of your passport, vaccine card, and boarding pass." You show up when boarding begins but the scanner makes an angry beep and they send you to the angry beep line to be reinspected for the third time. In the past you could look at physical boarding passes and see that yours did not have an extra stamp or sticker and get it resolved but here in the QR era there is no digital equivalent to clue you in.
Yeah, they really need to work on that. I'm not sure why they hide it. You'd think it would be a compelling reason to convince someone on a day pass to buy the full subscription.
Congratulations. On the one hand I'm disappointed that Delta no longer sells day passes, but on the other hand that's probably because their Sky Clubs would be overrun if they did.