the MS Graph Toolkit is a javascript library. there are two forms, the react library (used by the office team) and a web components library based on a new browser technology.
https://developer.mozilla.org/en-US/docs/Web/API/Web_components
this would be an alternative to writing a webform application. Instead you write a javascript app. a webform page can host an javascript application. for ajax to call the server, you would typically use use page webmethods, but you can add webapi support to webforms app and have the ajax call webapi methods.
the webform server can call the graphapi using the bearer token passed in the ajax calls. if the server needs to validate the token, then you need to add the owin middleware to your project and use its oauth support
https://learn.microsoft.com/en-us/aspnet/aspnet/overview/owin-and-katana/owin-middleware-in-the-iis-integrated-pipeline