Hi there!
I hope you are doing well.
Currently, there isn't any option available to save scanned PDF locally to the device.
However, you can save the scanned images to the photo gallery on your device.
Adobe Scan>Menu icon>Preferences>Save original images to the gallery
You can use the following link to share your feedback/raise a new feature request to the product team directly: https://adobe.allegiancetech.com/cgi-bin/qwebcorporate.dll?YQWCX7
To know more about Adobe Scan app, you can refer to this link: https://www.adobe.com/devnet-docs/adobescan/android/en/index.html
Let us know if you experience any issues, we would be more than happy to assist you.
Thanks,
Anand Sri.