A query that lists tags and has a column of all their associated tag groups?
That should be possible with something like this:
SELECT
t.name AS "Tag",
STRING_AGG(tg.name, ', ' ORDER BY tg.name) AS "Tag Groups"
FROM tags t
JOIN tag_group_memberships tgm ON tgm.tag_id = t.id
JOIN tag_groups tg ON tg.id = tgm.tag_group_id
GROUP BY t.name