Hi Stephen,
It's unfortunately is impossible in a single query filter. The reason being is (as you pointed out) that the 'Count' is not a field that can be queried and we can't get the size of how many tags are part of the artifact. We can find a specific value, we can also know if there are tags or not, but there isn't a way to query what you are asking.
Furthermore, you can't query the Tag endpoint either cause it doesn't point at the artifacts. The artifacts include the tags but the tag doesn't keep references to the artifacts it belongs to (otherwise, we might have worked it out this way).
You will probably need to break it to a few queries, or write a program using any of our tool kits where you can get and extract all the tag values and then use in-memory computation to figure out the tags size etc...
If you don't mind: can you let us know what is the use-case of this ask (perhaps we can find an alternative way to achieve it)? In other words: Why does it matter if a tag is exclusive or not?
Thanks,
Sagi