I want to add a feature to my template so that each time a user clicks the
bullet icon, the resulting paragraph has specific features, such as spacing
and indentation.

I've created bullet 1 and bullet 2 styles that behave correctly if the user
selects that style format from the style dropdown, but I want users to be
able to use the button and indent icons without having to select from the
style format menu.

Is that possible?