Applied for the personal "Premier Rewards" card June 30. No instant approval, got the "7-10 days" message. On July 3 received an email saying I had been approved. Finally, yesterday, July 12 (!) I received two envelopes from US Bank, one containing the card, T&Cs, etc., and the other containing a letter telling me about the credit inquiry they did. The latter tells me they pulled Equifax and my credit score was 757. (I've never before seen this in the context of an approval, only on a rejection.)
Prior to this I had no applications since November, although there were probably six or seven in the prior six months. I did not freeze the ARS/IDA although maybe I should have; I suspect that's why I didn't get the instant approval.