In my experience the new mortgage didn’t affect my Amex approval. I bought my house 2/19 and 4/19 was approved for an Amex. I was an Amex member prior to this app and yes my mortgage was reporting when I applied.
My Ex Fico at time of app was 690, so you’ll be in a better position then I was.
Some mortgage companies take months to report and some are fast so it may or may not be on your report when you apply. That being said if your scores are high 700s low 800s and your dti is not crazy high with the new mortgage I don't think Amex will even blink.
Scores hover around 800 Haven't been AZEO in over a year Rome was not built in a day, neither is a good credit profile