It would be nice if you could set the preferences in Adobe Scan to automatically save scanned files to a cloud folder, rather than having to "share" each scan individually. The automation would make this much more functional and user friendly.
Sorry for the delay in response.
When you scan a PDF and open it, you get an option to "Save as PDF" at the top right of the screen.
It will automatically save the PDF to Document Cloud in a folder named Adobe Scan.
For more information, you can refer this help link Scanning Documents — Adobe Scan Help
If you are referring it should automatically save to Document Cloud as a separate file when scanning multiple documents, you may fill the feature request for this feature here Scan iOS Feature Request and Bug Report Form.
Let us know if you need any help.