There is no difference (other than the signature of the f-droid.org version) in the case of SimpleX as it doesn't use FCM or any push provider, so there is no closed source libraries contained in any releases of the app and therefore no need for a separate variant

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f-droid.org and Play Store release should have a difference package name to avoid conflicts though

There are no Play Store or fdroid packages in the GitHub repo. Just the straight packages.

What would be the advantage of distributing packages built and signed by F-Droid elsewhere when the apps are functionally the same?

No idea. I have seen other projects that distribute fdroid and Google Play variants in their git repos, along with the straight package. I guess if you've already got the Google play or fdroid variant installed but want to start pulling from the repo, it provides an easy way to continue on without having to uninstall the old variant. Because sometimes if you have one variant installed and try updating to a different variant it fails, requiring uninstalling the old variant and then installing the new variant fresh.