Best Way to get count of Referenced Entities across collections

Your expected result should match the supplied source documents.

We do not know how to generated 2 different counts from the same name:newTag.

We do not know how you refer to Tags from your tags: because you do not share what you have in the arrays. It could be id or name. But is it id or _id?

Please read Formatting code and log snippets in posts

and then update sample documents and expected results.