In a few places I have read things along the line of this:

I am getting confused, because some people say this experiment has resolved the paradox and some people think its still a paradox. How exactly has the twin paradox "been verified experimentally" from the HK experiment?

The twin paradox is not really a paradox. People who still think it is a paradox are wrong, or misusing the word "paradox".

It is paradoxical only in the sense that it conflicts with some common intuitions or assumptions that turn out not apply. But relativity itself is mathematically consistent -- that is, it does not include any paradox.

The calculations that are used to calculate differences in the elapsed time for clocks that start out synchronized at a common location and then meet up again are confirmed to be accurate -- to within the available measurement accuracy -- by experiments such as the HK experiment. So it is not only internally consistent -- it is consistent with real life as well.

This doesn't mean all discussion about the twin "paradox" will stop. Every new generation students gets their minds blown by relativity, and needs to work through it for themselves. Just saying it is resolved by the HK experiment is not enough, because students will go on to try applying the calculations themselves, and getting it wrong by making assumptions that seem obvious but need to be explained.

We're here to help with that process, and it never stops.

LMAO. Thanks that has cleared up a lot i think. But what is it that distinguishes the twin paradox example from the HK experiment? The fact that twin is taking a different route and the commercial planes went around the world in a circle?

The twin puzzle (I'm going to call it a puzzle) is more idealized, isolating one aspect of the problem.

In the twin puzzle, there is one clock that stays inertial the whole time, while the other takes a longer spacetime path back to their meeting point. (And in relativity, the longest path takes the shortest elapsed time.)

In the HK experiment, there are three clocks -- or actually, three sets of clocks. (They used multiple clocks to help deal with issues of drift and keep a tab on measurement accuracies.)

NONE of them were inertial. Even the one that remains at one place on the Earth's surface is moving in a circle as the Earth rotates, and that has a measurable consequence. Furthermore, the HK experiment has to deal with gravitational dilation effects, since the clocks are at different altitudes. The twin puzzle abstracts all of that away, and has no gravity involved.