That is the correct answer. Also there is a lot of potential nuance, like evaporation or when you take the milk out of the fridge or the specific temperatures of everything, but under realistic settings adding the milk late will get you the colder coffee.

Does the ceramic mug become a factor? As in adding milk first allows the milk to absorb heat that otherwise would have been stored in the mug too quickly and then radiate back into the liquid over time slowing its cooling curve. (I have no idea btw I just enjoy trying to come up with gotchas)

I'd say adding milk late is the best. You have coffee with volume and heat V and Q, milk v and q. Whatever you do, you'll get volume v+V and heat Q+q. Q can become Q' if you let it cool down first, or (Q+q)' if you add the milk first then let it cool down. But because milk is cold, the Q/V > (Q+q)/(V+v), hence the loss Q -> Q' is bigger than (Q+q) -> (Q+q)'.

The best answer though is to put the coffee on a plate, and forget about the milk.

Isn't the answer milk first, then let sit? You only have 2 minutes, so if you're adding the milk after 2 minutes have already elapsed, then you've already exceeded the time limit, meaning the final measurement would take place before the milk is even poured in.

Adding the milk second is colder.

The bigger the temp difference the more cooling. So by putting the milk in right away you make the temp difference between the surroundings and the coffee smaller = less cooling over your 2 mins.

I like puzzles with a satisfying answer

Parent is complaining about being technically hotter because the time the temperature is read for logging is at 120seconds.

I notice this on HN more than places like reddit and Mastodon.

I think it's a benefit when writing requirements and programming to specs. It's less of a benefit when having a freeform discussion.