We shouldn’t mix the issues.
The second notification comes from the system not from F-Droid. How did you install the outdated app? As the client doesn’t work for you, I suppose you downloaded the apk from the website and installed it directly from the download folder. The system installer noticed that this app wasn’t built for your Pie device but for older Android versions, might be eventually inappropriate and prompted the message. (This is part of Android at least since Android 6, Marshmallow, and not a brand new Android Q feature).
The first mentioned notification however comes from F-Droid. As your device isn’t rooted the extension can’t be used and no apps regardless how old can obviously be installed.
The much more interesting questions to the devs of the client are:
- Why doesn’t the error message tell us the relevant things instead of some obscure description? “You installed the extension without root access. That won’t work.”
- Why doesn’t the client fall back to an installation mode without privileges when it is obviously capable to recognize the missing permissions.