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At this point the only way to add a class to an element on the page is to click on that element and move the mouse and click the Add Class Selector field in the styles pain.
I think it would be a lot easier to make a keyboard shortcut that opens the Add Class Selector field to quickly edit and add classes to selected element. Something like:
Shift + Alt + A opens the Add Class Selector field
This would let you immediately start typing the Class name without needing to move your mouse back up to the Add Class Selector field.