The Molly fork of Signal now has a variant that supports UnifiedPush, but it requires a helper called Mollysocket to be installed on a server somewhere. I can't get my head around the (we'll call them 'lean') docs, and I've never encountered such a helper for other UP apps. They just ask what to attach to, and they attach.
UP requires server-side support. Signal has ignored the request to implement it numerous times. So users need to host a proxy that uses Signal's websocket notification protocol to connect with Signal and distributes received notifications over UP. This moves the battery-draining websocket from mobile devices to some net-powered server.