Looks like non-Google Play downloads will be discouraged by Android 11
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Per a Google issue tracker thread (as reported by Android Police), installing APKs would not be so straightforward come Android 11.
On Android 10 and earlier versions, you are asked to okay an APK install, after which you are taken back to the app in question. You take off from where you left off.
Android 11, on the other hand, is governed by the Scoped Storage system. As the name implies, apps will only be given access to app-specific directories. As a result, the download process for non-Google Play apps has become a little complicated.
Per testers, when permission is now granted to an app, it is force-stopped. It's reloaded when launched again, which means background work and unsaved input could get lost. It would send out the impression that the app has crashed or it is buggy.
If it's any consolation, apps would be killed only the first time. Then once they have the specific permissions, they should work fine.
Prior to this, Android only used to force-stop apps when permissions were revoked. This is new behavior and an annoying one at that.
Here is what Google has said on the matter:
The way the filesystem and storage mounts are setup in Android R has changed significantly. When an app starts without this permission, it gets a view of the filesystem that doesn't allow writing to certain directories (eg Android/obb). Once the app has been granted this permission, that view is no longer accurate, and needs to be updated to a view that allows the app to write to certain directories. With the way the filesystem has been setup in R, changing that view on the fly is not possible. As mentioned in comment #16, we're evaluating internally. I'm just providing additional details why this doesn't work the way it did on Q.
Things that are NOT allowed: