highlights tool looks different on the smart previews

Ok, so a difference in using Smart previews vs originals

That smart preview is a  small, compressed, version of your original, meant to allow some editing when the optionals are not available, either accidentally or purposely, and to allow for some performance improvements as editing directly a smaller file is quicker. BUT their are drawbacks, sometime run into, sometimes not so bad. One being resolution, another being difference in edits compared to working with the originals.

Brought your RAW into my test catalog, and setup a Smart Preview copy. Altered the file names and file location as to easily look at both, and yep Ugly. I notice that it appears the depth of the Smart Previews allows for less movement in the highlights (yes, per LrC -100% but that is apparently relative). You can see this in the Histogram as well as the visual result

Incidentally, in your case, you altered the highlights, and had that very different result between original and Smart. You might notice if you alter the Exposure, a different result in terms of comparison Original/Smart will occur in both the Histogram and the appearance. Highlights effecting the brightest areas, Exposure the entire photo. LrC may be seeing less bright areas in the Smart preview due to a smaller data set. I suspect that different edits will result in less of a difference, and some just as bad. In this test case, adjusting the Shadows looks poor in comparison (not as bad, but noticeable)

I suspect an actual Adobe Tech, will state "As Designed"

Hopefully another member with color design knowledge will weigh in. Their is probably some math entering into this that such a member can clarify.

Can you repost more complete screenshots. it may be helpful to see the history panel, and it may be helpful to see the filmstrip and lower bar complete with file name, might be helpful to see Navigation panel.

Hey @Viktar Vysotski, 

A couple of questions to better understand what might be going on. 

1. Are you syncing images across Lightroom & Lightroom Classic? 

2. Does this happen to other images?