You are correct that the styling of most parts of Geany UI style is taken from the GTK theme so Geany "matches" the rest of the system. If your system does not provide a GTK theme it will use a default fallback that GTK provides. Anything in the style (not just font) you want to change for Geany only can be modified by GTK CSS in `Tools->Configuration Files->geany.css`.
The only fonts that have GUI settings are those Geany widgets, eg the editor, symbol list, and message pane that are application specific rather than theme specific.