Is there a cloud version of photoshop elements?

No.

A Cloud version would mean having the software stored and working in the Cloud (like the Lightroom Cloud version). That's not going to happen.

If you mean storing your media files and catalogs in the Cloud and accessing them from different computers, you can use web services like OneDrive or Dropbox. They create a special folder in your computer(s) which they 'sync' to the Cloud. The media files are accessible and sharable from any device like a smartphone, but there is no practical way to share catalogs.

https://feedback.photoshop.com/photoshop_family/topics/how-to-transfer-pse-2020-to-new-computer-current-computer-has-photo-files-on-onedrive