A version of this happened to me last year (my reason being forgot to set up autopay on a new account). I didn’t notice until the day after the due date. I made the payment, called the phone rep to explain and have them note it in my file, and everything has been cool with Amex then - approved for a new card and received a retention offer since then. So I recommend calling - I can’t guarantee it will prevent you from being dinged in some way but I don’t think it will hurt. I wouldn’t go into detail about the other cc payment, just indicate that you lost track of the due date in relation to other transactions on the account…

ETA: I would to see if your payment is actually showing up as late before making such a call. As you noted, the timing could work out fine in the end (and maybe that was what saved me rather than the phone call itself).I just wanted to provide some encouragement that all hope is not lost …