Travelling to the US as a spouse of a US citizen with ESTA and with the exemption outlined in the PP 10143?

I am a German citizen and I will be travelling with my wife (U.S. citizen) from Brussels (BRU) to the US. We both live together in Germany. I have an approved ESTA application. We got married in the US and have an American marriage certificate that we will obviously bring along. According to the website of the US embassy in Germany, this should be fine:
Q: Who is exempt from under P.P. 10143?
A: The following persons are exempt from P.P. 10143 and do not need an NIE (please note you still must have a valid visa or ESTA):
- Spouses of U.S. citizens and lawful permanent residents (LPRs)
- ...
Other family member relationships do not qualify for blanket exceptions at this time. Travelers in the categories above should contact the air carrier for questions about boarding requirements (including required documentation to prove your relationship).
The Lufthansa website states that to proof marriage, one needs a marriage certificate ideally in English. So this seems to be also fine (this is a code shared flight with United).
However, it seems some people on here had trouble entering the US this way:
- Someone got their ESTA cancelled
- Someone filled out a special form on the US embassy in Spain: This option does not seem to exist on the website of the US embassy in Germany
It seems the situation on this is evolving a little bit over time and differ between airlines and country one is travelling from. Does anyone has recent experience with this? I am going to leave this friday, so it would be difficult to apply for a B1/2 visa.
Update: Called the airline and they told me ESTA + marriage certificate is all I need and there won't be a problem. I am going to update when I actually made the trip.
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Can spouses of American citizens travel to the US?
If you are a U.S. citizen you have two ways to bring your foreign spouse (husband or wife) to the United States to live. They are: Immigrant visa for a Spouse of a U.S. Citizen (IR1 or CR1) - An immigrant Petition for Alien Relative, Form I-130 is required. Learn more.Can my spouse visit me on tourist visa?
Can my fianc\xe9(e) visit me in the United States on a tourist visa? The short answer is yes, you can. The same rules for spouses of U.S. citizens (as described above) also apply to engaged partners with a pending K-1 (fianc\xe9 or fiancee visa).Do US citizens need ESTA travel authorization?
All travelers intending to go to the US under the Visa Waiver Program (VWP) must obtain an ESTA authorization (Electronic System for Travel Authorization) BEFORE starting their trip.Can I enter the US with an ESTA visa?
An approved ESTA allows you to travel to a U.S. port-of-entry (generally an airport) and request permission to enter the United States, but an approved ESTA does not guarantee entry into the United States.The TRUTH about adjusting status after coming to USA with ESTA or tourist visa - Don’t buy the hype!
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Images: Ketut Subiyanto, Ketut Subiyanto, Uriel Mont, Karolina Grabowska