Entering the US after travelling with 2 passports

I have a few questions about a trip I'm planning to make to the US soon.

The background:
I recently moved to Mexico (where I am living now) from the UK. I have both Mexican and British citizenship.

On my way to Mexico from UK, I stopped in America as a tourist for 9 days, entering the US with my British passport under the Visa Waiver Program.
I then continued onward to Mexico using my Mexican passport.
I've been living in Mexico now for over 100 days (around 4 months).

I'm now planning to go visit the US soon, as a tourist for 2 weeks, using my British passport again.

As I understand it, under the Visa Waiver program I'm only allowed 90 days in North America, which includes Mexico. Since I've been living in Mexico for so long, I'm not sure if America will think I have 'overstayed' the conditions of the VWP as a UK citizen - despite my having Mexican citizenship.

My questions are:
Will be able allowed to go into America as a tourist again using my UK passport?
Will they accuse me of never officially having left North America after 90 days? Or will I be exempt from this rule because of traveling under my Mexican nationality?

And does the US have a record of me officially exiting the US, if I arrived into their country on a UK passport and then exited on a flight where I gave details of my Mexican passport?

You may know the answer if you apply for a new/update authorization (ESTA) to travel.

Why didn't you use your British passport when exiting the US?
Was your Mexican passport stamped on entry into Mexico?

For Mexican residents (therefore Mexican dual citizens) in Mexico, I doubt that time spent there would be included in the 90 days limit. Else, they can never qualify for the visa waiver program, as they may always be over the 90 days limit.

Thank you for your replies

For Mexican residents (therefore Mexican dual citizens) in Mexico, I doubt that time spent there would be included in the 90 days limit. Else, they can never qualify for the visa waiver program, as they may always be over the 90 days limit.

Yeah, that makes sense. I guess it might be safe to assume my time spent in Mexico won't count towards the 90 days because of my dual nationality, so maybe I shouldn't worry about that.

Why didn't you use your British passport when exiting the US?
Was your Mexican passport stamped on entry into Mexico?

My not using my British passport when exiting the US was a mistake on my part.

The US apparently does not have departure immigration checks at airports, at least not the way other countries do (though I did not know this at the time). I don't recall exactly what the procedure was, but I think all I had to do was use my Mexican passport that I used to book the airplane ticket to check in, and then get on the plane to Mexico, without a face-to-face immigration check being performed.

It would have probably been a lot smarter if I had booked my plane ticket using my UK passport, and then just showed the Mexican passport to Mexican authorities after landing in Mexico. But I fly a lot, and I'm used to booking flights with the passport I need to enter the country (since the airline can deny you boarding if they don't think you'll be accepted into a country). And usually, the immigration checks by the country I'm leaving give me a chance to clear anything up.

Having said that, I really didn't think this through at the time, and I feel dumb that I didn't realize I was potentially getting into a situation where America might think I never left

I did get my passport stamped when I arrived in Mexico, yes. Do you know if this would be enough proof at the border that I left the US, even if their system says otherwise?

Updating my ESTA is a good idea. That might give me a clue about if I can legally enter the US again. Thank you.