You shouldn't use Local Storage with Steam Cloud. Use File System writing to a dedicated folder.
If your game already uses Local Storage, you probably want to set up something like the following for backwards compatibility: use File System to write to a dedicated folder for Steam Cloud, but also check Local Storage for any older saves made that way, but don't save any new data to Local Storage.
I managed to save a json in the documents folder and then load it if it exists. I'm very happy, and more ambitious now..
It is now possible to export using WebView2 for Linux with Steamworks, in my case I use the tag for documents, in a Linux situation can I use the same tag or should I save the json in another specific Linux location?