Important Notice about v3.2.0
v3.2.0 posted here last night didn't get uploaded on Google Play at all. Apparently, Google is not yet ready to accept APKs with the new 'All files access' permission in Android R since they haven't setup a separate review process yet for apps that use this permission.

What's with this 'All files access' permission?
Swift Backup needs this permission to properly work on Android 11 (R). This permission gives apps proper traditional access to storage files as opposed to the restricted file access Google has introduced in Android Q and R. Google plans to control which apps can use this permission via Google Play Developer Policy.

So it seems like apps will have to fill a form and go through an additional review process by Google in order to upload APKs on Google Play with this permission in the Manifest file in the APK. From what I've read and heard so far, Google is planning to allow only File Manager and Backup Manager apps to use this permission, but I think other categories (eg. automation apps) will be included as well.

I will post an update here as soon as new information becomes available. Until then feel free to download APKs from @swiftbackupupdates.