I'm currently using the latest version of the GraphQL.Server suite. Specifically for this post version 4.4.1 of GraaphQL.Server.Transports.WebSockets.
For a while it seems most JS web clients have used the NPM package subscription-transport-ws which defines it's protocol to be "graphql-ws".
But even in it's code base It seems like this protocol is about to be deprecated
The subscription-transport-ws npm is now deprecated itself and the new npm that is suggested is called graphql-ws which has a specified sub protocol of "graphql-transport-ws"
As it stands now it seems that the most popular npm package to support GraphQL subscriptions today is not supported by this nuget package.