I also sometimes find new DMs in my messages here even though there is no dot displayed in the sidebar and no number at the top on the chat icon. Nevertheless, the “last visit” line clearly indicates that these messages are new to me.
But I have not yet been able to identify when this happens. The only thing I know for sure is that I was always logged out when this happened.
In my case, the user whose message didn’t trigger a notification is an admin, so I don’t think the fact that you encountered it with a new user is relevant.
Do you use the DiscourseHub app? I wondered if that is involved. If you don’t use the app, I could probably rule it out.