Re: VeriFly
App and review worked fine/quickly when preparing for my trip to the Bahamas several weeks back.
Departing from Philadelphia, I was told that I still had to go through the full check-in line. I showed VeriFly, but still had to show: passport, covid vax record, covid test, AND Bahamas travel authorization (which, like VeriFly covers all 3 documents). When I got to the gate, I was paged and had to show all of the documentation AGAIN. AA at Philly is a bit of a mess with procedures.
Returning from the Bahamas I didn't bother with VeriFly, showed my Passport and Covid test to the agent standing at the kiosk terminal, she handed me my boarding pass, I checked my bag, basically walked through security (PreCheck) and US Customs/Immigration.
Basically, app and review worked OK, YMMV on results depending on where you are traveling through ...