If a field is checked as Read-only in the composer, it will not be editable in the table. Fields that are not marked read-only will only become editable when the edit row-action is clicked. This would be the default Edit Rows Action with the pencil icon, or a Row Action you add back to the table as an Action Type of Edit Record. I was thinking there was an ‘edit row’ action in the action framework, but apparently there is not.
