This forum was so helpful for planning my trip, I wanted to be of help to others.
We flew out of DFW through Frankfurt and landed in Rome on 11/20. We flew Lufthansa, which may be a fine airline normally, but their covid document upload just doesn't work. We had to check in at the airport and show our vaccine card, negative test, and passport. No one looked at them again on the way to Italy after that. We went through a quick customs in Frankfurt, but they just looked at our passport and not at any covid related docs. When we landed in Rome, we didn't even go through customs and no one asked for covid related docs. We spent 4 nights in Rome, 3 nights in Florence, and 2 nights in Venice and took day trips to Naples/Pompeii and Pisa. Everywhere we went (restaurants, museums, trains, etc.) there was someone that asked to see our green card before letting us in. We had paperclipped our vaccine cards to our passports and most of the time as soon as we pulled our passport out they just glanced at the card and waived us through. A few people checked the cards thoroughly. Masks were obviously required indoors everywhere and they have people that will call you out if your mask slips on your nose a bit as I saw this frequently. This was my first time in Italy, and it seemed very crowded but I know that this was nothing like normal times. We were able to sit in the Sistine Chapel for as long as we wanted and there was very few people in there at about 9:30 AM. We heard few American accents. We flew home from Venice. I would highly recommend not to do that again. It is very hard to get to the airport in a timely manner early in the morning. We were planning to take the vaporetto, but then realized how long it would take. We tried to book a private water taxi the night before and it was too late to schedule it. We ended up leaving our hotel at 6 AM and walking to the bus station (about 15 minutes). We bought a ticket for the ATVO bus at the kiosk (which is more difficult to find than the ACTV kiosks) and hopped on the bus that took us directly to the airport. This was very easy to do and went very smoothly. Lufthansa's digital document upload did work for our return flight and asked for our covid test. We used the Binax Now with EMed and it worked just fine and was very easy to use. It is hard to do more than one at a time since it is a bit hard to hear. We did one and while we waited the 15 minutes on that one, started the next one. No one checked covid docs at the Venice Airport. We flew back Venice - Frankfurt - Houston - DFW on 11/29. We went through customs when we arrived in Frankfurt again. The officer just stamped our passport and didn't talk to us at all. When we arrived at our gate for the next flight, a gate agent was warning everyone that there must be a purple sticker on your boarding pass or passport or they aren't going to let you on the plane. We had used the app as our boarding pass and there was no purple sticker on our passport. Apparently, the customs officer was supposed to check covid documents and give the sticker. The gate agent was very nice when we explained we had gone through customs and where and showed the stamp. She told us she understood we wouldn't know to look or ask for it and that it was brand new. She checked our passports, covid vaccine cards, and our covid tests and then placed the purple sticker on the back of our passports and signed off that she had checked. We went through customs in Houston and covid documents were never mentioned.
We had a fantastic trip and I'm so thankful we were actually able to go. It was definitely more stressful than your pre-covid travels to keep up with the changing guidelines but at the end of the day, the stress was well worth it.