Certainly need to bring passport, vax card, negative test.
I would suggest, if you are using your app for your sea pass card, to get it retrieved on your phone before you get to the port, in case you have poor service. Adding to Wallet solves this as well.
I always print my sea pass cards, just in case.
I also make copies of my passports to take on shore, just in case, while leaving my passports in the room safe. On shore, I also take a copy of that day's Cruise Compass, which has contact information for the port agent.
I also make copies of my health insurance cards, and take on shore excursions, just in case.