I think this approach is quite okay. I suggested to have the UI like in the current version, since it doesn't hide everything in a menu, but there is at least the somewhat descriptive refresh icon and a visually clear way to access more options.

I'd remove the object icon from the menu item. It's reusing an icon for a different purpose, which we should avoid. In this case it's not adding much other than visual noise. It's well established that such icon use causes problems with no substantive benefit. (@Yevgeny Makarov (jenkm) made a nice writeup about such things on devtalk).

I think the menu entry communicates well without the need of an icon, especially since there is no other entries in the menu yet. If the menu becomes long then the render icon can be used but even then, the label is clear enough.

One small note perhaps a change in the tooltip "Create a preview for the selected data-block by rendering the active object", replace "data-block" with "asset"? From the user's point of view they are rendering a preview for an asset, the fact that it's a data-block is irrelevant. Also we can shorten the tooltip by using "this" since it's always in the context of the current/active/selected asset.

So it'd become: "Create a preview for this asset by rendering the active object".