The new wp_global_styles post type is registered to use edit_theme_options in the capability settings. The WP_REST_Global_Styles_Controller class's permission checks methods use the capability in a hard coded form rather than looking up the capability via the post type object. Changing the permission callbacks to lookup capabilities via the post type object, allows theme and plugin developers to modify the capability used for editing global styles via a filter and these values to be respected via the Global Styles REST API.
Props Spacedmonkey, peterwilsoncc, hellofromTonya , antonvlasenko, TimothyBlynJacobs, costdev, zieladam.
Fixes#54516.
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