I'm not sure why Steam's cloud storage webpage is not showing any of the saves, but it seems the same list is what is being sent to the Switch.
Try disabling cloud support for the game (in the library right click Divinity: Original Sin 2 and select Properties, then switch to the Updates tab and check the Steam Cloud section), exit out of Steam, use the Steam Cloud File Manager to delete the saves online (lsv and png files), restart Steam, enable cloud support again, start the game, load the latest save and resave, then exit and make sure at least the new save is synced online.
Check the website first, and if the lsv files shows up, at least, try syncing on the switch.
If that doesn't help, restart the Steam version, create a new profile, start a new game and save when you get through character creation, Alt-Tab out of the game and copy the 3 quick saves to the new profile, switch back to the game and exit (if necessary restarting to get Steam to sync). If Steam only syncs the new save, restart reload the most recent quick save and re-save again.
If that still doesn't help, check the 'C:\Program Files (x86)\Steam\logs' folder for the cloud_log.txt file, and upload it to Dropbox, etc, to reply or PM with a link, or include the contents between 'spoiler' tags (in the same format as the 'img' tags above).