@julienGrd you should be able to use a runtime check to determine if you're executing in a Blazor WASM app and use that to conditionally register a service as a singleton:

if (OperatingSystem.IsBrowser()
   services.AddSingleton<IService, MyService>();
else
   services.AddScoped<IService, MyService>();

Admittedly it's not a great way to go about it, but this is also the first we've seen any feedback on this, so we'd like to wait to see if we'd like to tackle this more broadly.

@pranavkm thanks for your help. Actually the problèm is focus on the server part (even in webassembly mode). There is nothing related to the client. And its not really related to blazor, more to asp .net core.
If i Can resume what i need, there is a way to make a scoped service on the server with a lifetime depending of the session of the user ? Actually thé scope is per request when i run in webassembly mode, but works perfectly (by connection so by "session") when it run over signalr.
Sorry if im not clear

Sorry if I'm not following along, but is the ask to have a service that is tied to a user's session? For a Blazor Server app, you should get this by default, and infact slightly better than vanilla SignalR since a scope is tied to a circuit which can exceed a single SignalR connection.

For a Blazor WASM app, a singleton service would be the closest approximation - a user is in session as long at they have the Blazor WASM app running. If you meant to have it actually tied to a browser session and survive app restarts / browser refreshes, unfortunately there is nothing in the framework that solves this. The closest would be to stash data in the browser's sessionStorage / localStorage and use that to recreate your services as part of startup.