Cross-save allows you to access the data from your active account, Xbox in your case, across all of your linked platforms. The data does not transfer to the other accounts, and it will always be permanently tied to your Xbox account. It is correct that your Steam account will show as having no characters, because you do not have character data on your Steam account, and are using your Xbox data to play the game. Regardless of what platform you are playing on, the save data is in fact Xbox data. This means that you need to be looking at your Xbox account, not your Steam account, when using the companion app, or third party sites.