@leo this is what proves that the APK was indeed built from the very same source it claims. Cross-updates are possible when the same signing key was used in those places – which implies that the app must be set up for RB at F-Droid as well, as otherwise F-Droid uses a key they generated (and then, cross-updates are not possible).
Signing ensures that updates are only accepted when the same key was used, where only the owner knows the credentials for.