There is no way to define margins for the icon in the Button class (as far a I know).
The buttons look awful without space:

I could offer myself to implement a proper solution for this but I'd like to hear some feedback about this. If there is a way but it is undocumented I could add it to the docs.
It would be good to know if there are more Controls with this problem.
After searching I've found this issue but it's pretty old and I'm not sure it is a good solution.
Margins and being able to pick the position (at least left or right) would be really nifty, yeah. Although I don't know if this is something that should be themable, a setting per button, or both for maximum flexibility
If you have custom stylebox for the button, you can define a content margin for each side.

Maybe this just needs to be documented somewhere. I don't think there's need for a new feature.
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If you have custom stylebox for the button, you can define a content margin for each side.

Maybe this just needs to be documented somewhere. I don't think there's need for a new feature.