It may not be a hard pull, by logging into my amex account, I got a message on my app that I'm pre-approved but i think it would still show up as a new account which counts towards 5/24... Correct me if I'm wrong
Hard pull and 5/24 are completely separate. Any card that reports to your credit, will count towards 5/24. There may be some exceptions, but thats the general rule, regardless of whether they pull