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.
They do have e2e for emails. Any emails between Proton Mail users are always e2e encrypted, as are any emails others send you which they’ve encrypted with their own maio client. If someone sends you an email unecrypted (most email is), then Proton will encrypt it for you and put it in your inbox. They can’t read it after that, but there is some trust required that they don’t store/look at the unecrypted email before then.