To enable save synchronization in the game, users must switch GameHub from a “lightweight” Steam mode to a numbered version. This option can be found within GameHub under the section labeled Silksong. Users should select the three-dot button, navigate to PC Game Settings, and make the appropriate selection for Steam.
Once gameplay has concluded, it is essential to trigger an upload of the saved data. This can be done by swiping left on the right edge of the screen. Afterward, users should click on the gear icon and select the Exit option. A notification indicating that the save is uploading to Steam should appear, and the upload process is typically quick before the game fully exits.
Source: https://www.theverge.com/pc-gaming/777551/gamehub-fixed-its-silksong-save-game-uploads-and-now-im-playing-across-phone-and-pc