markets.books.microsoft

"... However, it seems that the Edge browser still tries to access this certificate thus the false positive."

Is it a false positive if the certificate has actually expired?  I don't think so.  It might not be a malicious connection, but it DOES have an expired certificate, which is exactly what Bitdefender says.

Well we know where at least some of the requests come from, mine is when I log in to Office 365.  Why would that action require my computer to access books?  And yes, Microsoft CAN change their login procedures to stop them referencing their own outdated site.

No, since it's the Microsoft Windows Store or Microsoft Edge attempting to communicate with the unsafe, unsupported Microsoft site, Microsoft should fix Microsoft's annoying, huge problem.  See the key there?  Microsoft.  Bitdefender is not in charge of Microsoft's apps or expired certs lol.

Just because edge is attempting to access the url doesn't mean that edge is initiating the command. It may be that a third party app is attempting to access the app and because edge is your default browser, then that's what it uses. It's bitdefenders job to recognise a dead link and suppress warnings from it. MS can't be expected to keep a cert updated to a dead site

No, Office 365 is initiating the command.  So it's STILL Microsoft's problem.  And ONLY Microsoft can fix this.  Edge isn't my default browser, but if I want to open Word 365 (e.g.) it opens in Edge, even though I want nothing to do with that browser.

It IS safe to do so! I ran a scan with Bitdefender after allowing the exception, and no malware was found. Lots of certificates from legitimate websites and links are not updated sometimes. You just  have to research a bit. Microsoft uses that certificate, but apparently haven't updated it. It's used for their apps and programs. I found a Microsoft webpage that explained what that certificate was used for. Only when I allowed that certificate the exception, did my emails in Outlook 365 started coming in. I was frustrated for a week trying to figure out why my emails weren't coming in through 365! That's exactly when the certificate error started showing!. I tried EVERY process I could find to fix Outlook! Apparently, Outlook 365 uses that certificate. 

Outlook runs fantastically now, and there's no ill effects on my system. It's your call. 

I don't think the issues is about a certificate being expired or whether bitdefender thinks it malicious or not.  The issue is WHY does MS Edge keep trying to access the site in the first place when I don't care about that site or have any reason to connect to it.  So for me the question is "How do I stop Edge from trying to access markets.books.microsoft.com

I have never used it either and when Bitdefender 2020 popped up a warning, and so I chose to block it. Hopefully that's the solution to the annoying repeats issue.