How to logout of the Apps Store in Catalina, and login using different Apps Store ID than that of the Apple ID

I got different IDs for Apple ID and Apps Store since years ago; and I reluctant to use the same ID for the Apps Store as for the Apple ID, since most of my purchases were done through that (different) ID.

My issue is after reformatting the Mac (yes, I did that), I could not find way to login into the Apps Store using that different ID.

It is not a simple logout of Apple ID and login with different ID, as what I need to log out is just the Apps Store and not the Apple ID.

I somehow could not find the answer in this Apple Community, as the answers were not filtered by Mac OS versions, thus answers as available were somehow outdated. The solution is simple (I believe that), just that I do not know how.

Please assist. Regards.