In the ashx.cs file, also “implement” the interface System.Web.SessionState.IReadOnlySessionState or System.Web.SessionState.IRequiresSessionState.
You don’t have to implement any method, just the presence of this makes the Session available (in readonly or read/write mode), through context.Session.
The header would look like:
public class MyHandler: IHttpHandler, System.Web.SessionState.IReadOnlySessionState