ESTA and multiple nationalities + using different passports at check in and immigration [duplicate]

Just signed up and this is my first question.

I have recently become a citizen of Australia and will be traveling back to the US again soon. I already have an ESTA on my European passport however now that I am Australian too I have to use this passport when traveling in and out of Australia (this is apparently mandatory for AUS immigration). Do I have to apply for a new ESTA on my Australian passport to now travel to the US or can I use my existing one on my EU passport? Am I able to check in with the airline when leaving Australia on my EU passport but then show my AUS passport at Immigration when exiting the country and then show my EU passport when landing in the US? Or do I need to use the same passport for both?

There seems to be conflicting info online. A similar question was already asked on here but the only answer to that did not offer clear explanation. My question also refers to checking in with the airline on one passport and showing immigration another passport and whether that is ok or not.

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Can I have two estas in different passports?

No. Each Visa Waiver Program traveler must have an approved travel authorization for the passport they plan to use before they travel to the United States. If a traveler obtains a new passport, they must submit a new travel authorization application in ESTA using the new passport.

Can I leave the US with one passport and enter with another?

Most U.S. citizens, including dual nationals, must use a U.S. passport to enter and leave the United States. Dual nationals may also be required by the foreign country to use its passport to enter and leave that country. Use of the foreign passport does not endanger U.S. citizenship.

Is ESTA linked to passport?

An ESTA approval is always linked to a passport and the corresponding passport number. Since your new passport will receive a different passport number, you will need to submit a new ESTA application.

Can I have two passports from different countries with different names?

Thanks... Answer: There is no guarantee that you would have problems using two passport with different names in them but it is quite likely that you will. Passports should be used which have your current legal name in them.

Traveling with two passports - I almost got arrested | Jure Sanguinis Italian Dual Citizenship

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Images: Keira Burton, Gustavo Fring, Anna Shvets, Field Engineer