It'll save when you go to the hut, and it'll sync when you attempt to close the window (don't leave when it asks you to stay) or click Sync Now on the title page. Try clicking sync now, and see if there are any sync failed errors.
The full version is in early access: https://store.steampowered.com/app/876650/Aground/ , and you can transfer your saves by exporting/importing them from the options menu on the title page or using Aground Cloud.
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It'll save when you go to the hut, and it'll sync when you attempt to close the window (don't leave when it asks you to stay) or click Sync Now on the title page. Try clicking sync now, and see if there are any sync failed errors.