Welcome to the community, @Matt_Rogowski! :grinning_face_with_big_eyes: The color assignment for single- and multiple-select fields is just an extra bit of styling that Airtable applies to the field itself. When referencing those field types elsewhere, Airtable only passes the data, not the associated styling. To my knowledge there’s no way to access this styling info, not even via the API.
One way to add some color to such fields in a form that will stick with it elsewhere is to use emojis as part of the selection definitions.