The UnifiedPush server is intended to be a single source your phone can keep a persistent connection open to, rather than needing a connection per service/app (this is how Google’s Firebase notifications work too).
As Signal doesn’t support UnifiedPush, MollySocket keeps a permanent connection open to Signal’s servers to listen for new activity and forward them to your UnifiedPush server. This saves your phone keeping a permanent connection open to Signal’s servers and draining your mobile battery more.
Another recommendation for Proton Mail. As others have said I’d recommend getting your own domain for email so you can always migrate providers without having to change your email address.