How do I move the Field Accessibility settings?Under each field you will see 2 types of settings.
Field-Level Security: This controls the access of the profiles to the field.
Field Accessibility: This depends on the access of the profile and the visibility of the field in the layout
In order to move the Field Level Security, you just need to move the Profile and the Field.
In order to move the Field Accessibility, you need to move also the layout since the Accessibility depends on the FLS setting and visibility of the field in the layout.
So basically, the Field Accessibility is the result of the access to the field considering the access for the profile (FLS) and visibility in layout.
If you create a field in source org and move only the field and profile to the target org, you are moving only the FLS and the field will not be visible in any layout in the target therefore the accessibility will be always Hidden because of the page layout.