I do concur that the Harmony rules would be greatly improved with those previews and hover support.

Not quite sure why I chose Theory instead of Harmony. Perhaps there's because there is a lot of color values within the color wheel to pick from at random, and by adding the color harmonies to convert the artwork to be harmonious, that would be one way the user could ensure they have a smarter selection of colors, and still follow the same workflow in the recolor artwork panel.

Here's a more lengthy prompt engineered output, that still includes complex color tools :

Might have some drift in it.

Might be unnecessary, but I think it would be helpful to see it.

Scientific Swatches are not exactly harmony rules I meant. These are just fixed set swatches, and you restrict colors of your selected artwork to these set when doing it. Can fit some tasks, but these are rigid.
Color Harmony presets I meant work differently and take your actual colors into account as a base: https://helpx.adobe.com/illustrator/using/color-groups-harmonies.html

The idea with yet another button (to make the Recolor dialog even more complex?) is worth thinking of, but it doesn’t really differ much from picking these harmonies from the preset dropdown. Two entry points for the same thing, separated from each other, would make it even more confusing to locate. Plus hierarchically it belongs above the list of colors.

What I’d agree with is that the dropdown with Harmony Rules needs a caption... and scrolling when unfolded working, and scrolling on hover support, or even having it taller when a screen allows to.

'Random Color Based On Color Theory' in Advanced Options under Advanced Options.

Great share. Thank you for the opportunity to explore it further with you.

After further Inspection I have rediscovered the Scientific Swatches within the Color Theories as described.

Thinking further into it, there are some randomization buttons, like Randomly change saturation and brightness. I wonder if the scientific color theories could be integrated into the higher order within the randomization of brightness and contrast to save on some clicks, or this idea :
Perhaps a 'Randomly changes color based on Color Theory', which would be a combination of the outputs one might encounter from the Scientific Color Theories dropdown.

How exactly this 'automatically' should happen?
Recolor Artwork dialog (the advanced mode) allows us to use Color Harmony preset, and then pick the rule from the dropdown at the top.
What do you want to improve with it? Please elaborate.