I’m a little confused as to where to control the settings. There is the ‘customizer’ menu within WP and there is your theme settings menu. It seems that for some changes it has to be made in customizer when others have to be made in theme settings and yet other changes needs to be made in both? Could you tell me which type of changes should be made in which settings menu?
Please specify which menu changes do you mean and what menu. It is typography, you will go to the Theme Settings > Typography, if you want to add/remove menu items, you will go to Appearance > Menu
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