This is the only way I can see of excluding tags from a search.
It is possible to search for tag groups by using the category modifier with the tag group’s slug. For example, if you had a tag group called ‘topic status’, you can search for its tags with #topic-status, but tags can’t be excluded in this way, so -#topic-status doesn’t work.
Sorry, I wasn’t as clear as I could have been. If it was possible to exclude a tag group from search, this approach would work, but I can’t see any way to exclude a tag group from search results.
You could get a list of topics that only have a single given tag with a Data Explorer query. Something like this might work for you:
--[params]
-- string :tag_name
with tagged_topics AS (
SELECT
topic_id
FROM topic_tags
JOIN tags
ON tags.id = topic_tags.tag_id
WHERE tags.name = :tag_name
),
counts AS (
SELECT
COUNT(id) AS tag_count,
tagged_topics.topic_id
FROM topic_tags
JOIN tagged_topics
ON tagged_topics.topic_id = topic_tags.topic_id
GROUP BY tagged_topics.topic_id
)
SELECT
c.topic_id
FROM counts c
JOIN topics t
ON t.id = c.topic_id
WHERE t.deleted_at IS NULL
AND t.archetype = 'regular'
AND c.tag_count = 1