I forgot to add to this, but my notification badge Microsoft Account/Back Up Reminder issue thing in the Start menu that I was asking about initially (all related to my local account), got resolved the moment I went to Settings > Start and scrolled down to Others, turning the toggle off for "Show Notifications related to the Account". It was as easier as it was mentioned elsewhere and the headdaches related to this specific nagging were luckily erradicated. It was, definitely, an ad.
As I mentioned earlier, I conflated MSA<-> OneDrive, and that confused me when I wrote the original post and I wish I could have been able to edit after I realized. What keeps intriguing me is that, I have this computer with Windows 11 since almost two years and just quite recently it started to do that specific "nagging". Might understand Microsoft insisting to a local account's user to get into a MSA to get OneDrive (especially in Explorer), perhaps, but I never imagined they would ALSO insist about attempting to make you switch your mind about preferrably using a MSA, in the Start menu.
