Final update:
Removing Substance 3D Painter from Adobe Cloud Desktop finally resolved the Access Denied issue.
For the error when clicking directly on projects, I forced a solution by setting Steam's Substance 3D Painter.exe to always open it. This involves the cumbersome “Launch game with custom arguments” prompt where I have to grant permission each time, but I'm not in the mood to discuss that problem right now.

And here's the most crucial point: the issue where projects fail to open and data vanishes due to version mismatches remains unresolved.

Launch Substance Painter → Open → Click on a saved project, and it opens without issue,

but

clicking the project directly displays:
"

Access Denied

You don't have permission to access "http://commerce-stg.adobe.com/store/segmentation?" on this server.

Reference #18.23f7dc17.1766869289.1ff29eb2

https://errors.edgesuite.net/18.23f7dc17.1766869289.1ff29eb2

"

Uninstalling and reinstalling does not fix it.