I did not try to install my copy of Adobe Photoshop Elements 2020 on my M1 MacBook Air. I did purchase and install Photoshop Elements 2021 a few hours ago. It works just fine. I believe there are a couple of edge case scenarios where bugs have been found, but Adobe is working on those.
For my workflow, Photoshop Elements 2021 is running perfectly under Rosetta 2 on the M1 MacBook Air. I'm very happy about that.
I did also purchase Pixelmator Pro, which is running as a Universal App, and I like the features that it has as well.
Lee
P. S. Here's an excerpt from Adobe's support website regarding Photoshop Elements 2021 and Big Sur:
Known compatibility issues with Photoshop Elements
Adobe has discovered the compatibility issues listed below with running Photoshop Elements 2021.0 with macOS 11.0 (Big Sur).
Disk error
When you select Enhance > Colorize Photo, you get the disk error. We are working to address this issue.
Photoshop Elements creates a blank canvas
When you copy an image from Elements Organizer and then select File > New > Image from Clipboard, Photoshop Elements creates a blank canvas. We are working to address this issue.