It was so frustrating that whatever I tried, no fix helped. I had a final idea which seems to have solved the issue for me. At least I hope so, we will see in a few days I guess, but so far, it seems to be working.
Since Microsoft Apps were nagging about SSO I thought about what would happen if i actually unliked my Microsoft account from my windows account and turned it into a local account instead ( Settings / Accounts / Your info --> Sign in with a local account instead.
After I logged back in with a local account, I had to enter my microsoft account credentials into most MS Apps once more (Edge, Office, OneDrive...). I rebooted quite a couple of times today and did not have to enter any MS account credentials (or SSO verifications) anymore.
If it really keeps on staying this way, I'll just live with like this, since there is no big advantage in using an MS account within Windows anyway (especially if the alternative is having to deal with re-entering credentials every single time).
If it should not work anymore within a couple days, I'll make sure to reply to my post to let you guys know.
Back for report. It's been a couple of days and my issue seems to be fixed with the workaround I've applied.
For clearing things up, in case someone didn't quite understand my thought process behind the workaround:
Microsoft is nagging us about an SSO login, which in short means that it is trying to automatically log you in into services using your existing MS account, which is currently logged on in your Windows instance. This normally allows you to log in much faster into applications, as it is using your credentials automatically from your current session. Since the SSO part is nagging at the moment, I unlinked my Microsoft account from my Windows account and I'm using a local account instead (which can be done in the Windows account settings - a quick google search will show you how to do it).
Since I am logging in with a local account to Windows now, like in the good old days, there is no more SSO login happening with other MS services, such as Edge, Office and OneDrive. Instead of using SSO, I now need to log in into these services individually - using my MS account. After logging in into these accounts one final time (without SSO), the issue was fixed for me.
Beware though: Upon logging in into the services individually, Windows may ask you, if you want to link your MS account to your Windows account. The prompt might come in different ways like "do you want to sign in into other services automatically" (I'm not paraphrasing here). It's important to neglect these kinds of prompts in the future, until the SSO issue has been fixed.
Hope this helps someone out there.