We flew out on AA about 3 werks ago. It was a madhouse! Lines going everywhere. We had our documents loaded in VERIFLY. This allowed us to skip the 1st crazy long line that they had setup to check documents (before you are allowed to stand in crazy long line for checkin and crazy long line for security). They had a person checking your phone for VERIFLY approval.
If we had to stand in 1st line to check docs, it would have added 30-40 min on top of the 1.5 hrs it took to clear the checkin and security line.
With Omicron, expect even longer lines as people are out sick. Get there early (we got there 2.5 hrs early and had 30 min before we loaded).
Like DD said, I don't remember anyone looking for my vaccination card but, you only attested you were vacinated on one of the documents.