it's most likely a bug in their system. Given that is just an annoyance more than a real problem I would expect the priority to be veeeeeery low, so don't keep your hopes to high on a resolution. I've given up wondering what type of notifications are those. If they were actually important, Garmin would've gotten their act together by now.
Me too - they appear not when I log in but if I've left the browser inactive for a period of time and as soon as I refresh the screen or switch to another tab/screen within connect they disappear. Given the level of inconvenience (i.e. very low) I can understand it being low on support's priorities - particularly when the new Garmin connect implementation seems to be falling apart around their ears :)
This doesn't seem to happen in Modern, only in Classic. I assume they fixed it for the new look Connect and because everyone will be switching soon they haven't bothered to fixed it in the classic view