Upvote:3
As noted in the comments, the ESTA application asks you about passports from other countries, so your passports will be linked. Maybe you're thinking that if you don't tell them about the passport, they won't notice. Maybe you're right about that, but if you're wrong you will be indefinitely inadmissible to the US for deception. This inadmissibility remains until you apply for a waiver, but only if the waiver is granted, which is unlikely.
So you really don't want to lie on the ESTA application unless you're prepared to accept never being able to go to the US. What's worse, if you don't tell them about your other passport in the application, they might not make the connection until you actually present yourself at the border, at which point they will surely match your fingerprints or your face to their records. Then not only will you be banned for deception but you will also have your day ruined (if not your entire planned trip) by being denied entry at the border.
Your ESTA will probably be denied. Even if it is granted for some reason, as someone who has previously overstayed under the visa waiver program, you are in fact no longer eligible to use the VWP/ESTA (I believe there is some provision for people who overstayed because of COVID-19 to be excused from this ineligibility, so if that is your situation then you might want to look into that). If you manage to get an ESTA, therefore, even after answering all the questions truthfully and completely, there's still a risk of your being turned away at the border. Your best bet is to apply for a visa.