When an update notification message appears, it apparently gets assigned to one tab which is not always the active tab. When this happens, the update notification message steals the focus and prevents me from interacting with the active tab. For example, I can’t type anything into the address bar. The browser appears broken/unresponsive. In order to continue using the browser, I need to guess that an update notification message has appeared, switch tabs until I find which tab the update notification message has appeared on, and then dismiss the update notification message. I consider this to be a bug.
In my opinion there would ideally be an option to stop these update notification messages from popping up altogether, even if they are not assigned “invisibly” to an inactive tab, since the fact that they steal the focus, pop up covering the content of the page you are viewing, and (at least in previous versions of the Tor Browser, I don’t know about the current version) sometimes pop up multiple times in the same session make them obnoxiously intrusive and detrimental to the user experience. I am sure that a less instrusive notification system is possible.