On my mobile menu when I click on the category name, I’d like to drill down the sub categories instead of go on the category page linked directly.
Means to have the same behavior on category menu label (red square part on sreen shot) as the arrow behavior (green square on screen shot)
There is no option to disable the links. You can apply a trick by creating the menu items for the mobile categories menu using Custom Links in Appearance >> Menus and set the URL to #.