Here's what I would expect...
The first group of 5 areas (OS Update/Plugins update/Docker update/Language update/Array status) are specifically defined areas that can be enabled/disabled completely. I believe this happens without regard to whether the notification is a notice, warning, or alert.
However, plugins and other areas of the OS can also send notifications. For those, you can enable/disable notifications based on the severity (notice/warning/alert)
If you are seeing something different please provide your diagnostics.zip (from Tools -> Diagnostics)