I can confirm my test account only received a notification on the one article they had access to!
I also got an error when attempting to send a notification for a private article with no subscriber group, which is much appreciated! My one bit of feedback is that the error read "make sure your article is published", which it was. The actual problem was not having a subscriber group. If feasible, the cherry on top would be if the error could be more accurate to the problem.
Either way, this bug looks to be fixed and this can be closed. Thank you so much for resolving this so quickly!