The current version of MM (2021) is 29. Is that what you have (you can check under Help>About)?
If so, and you really did previously have MM16, rather than MM 2016, you have skipped 13 versions and, over that period of time, there have been a number of changes to MM, not the least being that the latest version is 64 bit, so the problem of projects not loading is not really a surprise.
However, if you previously had MM 2016 then please give us rather more detail about what actually happens when you attempt to open an old project in the new version.
One thing to note (and this is catching out quite a number of users): because MM 2021 is the first 64 bit version of the program it is, essentially, a "new" product and to gain access to all its features the user must pay the upgrade fee forthe upgraded version. Merely updating (without any payment) means that the new version is actually the Free variant, even if you previously had one of the paid-for variants, i.e. Plus or Premium.
I did have MMM2016 premium but I was not made aware that I would not be able to load my projects without a fee. I chose to replace MMM2016 and so now nothing loads on the new version. It was advertised as an update and not a purchase.
I chose to replace MMM2016 and so now nothing loads on the new version. It was advertised as an update and not a purchase.
This is true and it was very poor stuff from Magix. Replacing is a bad choice and Magix should have provided warnings. I think you need to reinstall MM2016. You should find a download link on your account page.