To get save to sync to begin with, you’ll need to flick GameHub out of a “lightweight” Steam mode and pick a numbered version instead. Find it in GameHub under Silksong > hit the three-dot button > PC Game Settings > Steam.

To make sure you trigger an upload when you’ve finished, swipe the right edge of the screen left, hit the gear icon and pick Exit. It should say it’s uploading your save to Steam, and it shouldn’t take very long at all before the game exits.