In my experience HTTP/2 doesn't boost proxy performance significantly, at least for HTTPs workloads. Normally the client sends a single CONNECT [hostname] request to the proxy and after that the proxy just forwards TCP packets on that connection, which is nothing that HTTP/2 can improve. A client can of course use the same HTTP/2 connection for multiple CONNECT requests, but opening several data streams to the proxy in parallel isn't much more costly as those streams tend to be long-lived and will often carry multiplexed HTTP/2 connections themselves, so further multiplexing on the proxy level often has little effect (in my experience at least).
Regarding QUIC/MASQUE it's still difficult to find any clients that support it. I think Chrome supports using QUIC to connect to a regular HTTP CONNECT proxy, but I don't know of any browsers that have even experimental support for MASQUE as of now. Will be pretty great tough I think once it's supported more widely.