Recent travelers returning from Europe? Looking for Up to date Covid rules:

For unvaccinated people from the States, Germany has just issued a 10-day quarantine.

I just returned from Germany yesterday - though I was only there for 1 night in transit. No issue getting in but as Bets said, Germany has now introduced stricter rules starting yesterday for Americans especially if unvaccinated.

It's complicated.

First, as others allude, guidance out at the moment is in place for the remainder of August for the most part, each country will then modify that guidance for another 30 days or so.

Be most concerned about air travel, since authorities will be looking at passports and putting checks in place. What matters most is where you are coming from, not your Nationality, and then where you have been in the last 14 days, so a couple weeks into your trip, you will be subject to restrictions placed on 3 or 4 countries, though restrictions for most EU countries are similar.

Even crossing a border by car, you are still required to meet any requirements, even if nobody may check. You will register at a hotel, and that information goes to the police or authorities, they could follow up, or police may stop cars with out of country plates.

You can go here, https://www.iatatravelcentre.com/world.php to get information on up to date measures, just click on the country.

If you are traveling with children, that presents a possible gap in requirements. Since "under 12" cannot get vaccinated, in some places they are required to test, and may fall into quarantine requirements. Many places do exempt under 6 years old, so those 6-12 year olds are the "gap".

Of course, returning to the US, at this time you need a test...vaccinated or not.

On a side note, if AA is American Airlines it's not your carrier between Budapest and Hungary. AA1 doesn't fly within Europe. It's probably a code share and you need to see what airline is actually flying it. It's on your ticket/itinerary.

If it has an AA flight number it's probably Iberia as they are in the same alliance.

We are trying to list the official information sites here: https://community.ricksteves.com/travel-forum/general-europe/a-few-countries-are-trying-hard-to-make-it-easy

Honestly, it changes EVERY day in almost every city as well as in every country. We who live here can barely keep up with what regulations are in effect each day, cause they keep changing, practically every day. I check the news every morning to see what the incidence rate is for Frankfurt, then for Hessen, then for Germany.
Trying to keep track for 6 countries ahead of time is nigh on impossible. You are just going to have to be flexible and ready to change your plans last minute.

For Germany, recommend reading the online version of DW, as they have up-to-date news for Germany.