where will I find 2021 and 2022 badge albums?

They are in classic view.
Click on your avatar / My profile / hit the Gear / Back to my collection. 
That should get you there.  😀

Or in new Pogo click your avatar / my profile / classic library / browse albums

@fadedwildrose:  My Collection, My Gifts and My Minis are still under construction (at least on my page..).

You can still click on them even though they are under construction.