Is there any way to get this value from Discogs into a field in mp3tag? For example, I would like this field to be populated with the artist_id value from Discogs when I use Discogs as a tag source in mp3tag.


You have to adjust the used discogs.inc or discogs.src websource script text file in your Mp3tag configuration subfolder \sources.
If you open this file, you will see that this is unfortunately not an easy change that you can make in a couple of seconds.

(A Websource Script is parsing the result answer from Discogs and tries to catch the exact position of such a field and assign it to a tag like your proposed artist_id.)