Unfortunately there's no way to sync purchases between different platforms. Google Play Store, Apple Store and Steam are different services by different companies. Only store that allows to "sync" is humble store, which allows to add steam keys.
The updates will now happen automatically once you move to the Steam version! The Steam version comes with cloud saves, auto-updates and many more nice changes in the future. If you didn't find a download link in your email, try to resend download link via this form: https://www.humblebundle.com/resender