Remember that it is the P/E ratio. So, it goes up when prices go up, but it also goes up when earnings go down. And having closed a year when, say Norwegian Cruise Lines lost $15.75 a share, that is going to look bad. And this year, while "recovering," won't look good on the basis of annual earnings, either. And Case Shiller will live with that for 10 years.
And that's part of the point: to get a PE over a full business cycle. Should a pandemic year be declared an outlier, and either struck from consideration, or turned into a footnote for every interpretation? Or is it a realised potential, and it could easily happen again? If it did happen again, would we recover slower, faster, or about the same?
Or maybe it's perfectly valid, since the general assumption is that business cycles should last 5 years, and we just finished the longest bull run ever. So a recession That's "twice as bad" just evens things out?
Until you have thought your way through those questions, I don't think you can conclude anything on the Case Shiller PE.