The Customizer doesn't use the admin_body_class filter

[afercia]

The ​Customizer doesn't make use of the admin_body_class filter. I would expect all admin pages to use it.

Rationale: plugins may want to add their own CSS classes for their own purposes.

Actually, while developing a small plugin, I had to resort to the customize_controls_head action hook and add my CSS class via JavaScript. It is a workaround but it's not ideal.

Wondering if there is any specific reason why the Customizer doesn't use the admin_body_class filter.

Trac ticket: https://core.trac.wordpress.org/ticket/65796#ticket

## Use of AI Tools

None

Tested well!

The custom class my_custom_class appears correctly after pulling the changes from this PR.

### Before:

### After:

Thanks for your review @mukeshpanchal27 I would like to hear from @westonruter if there's any reason to not do this we may be missing.