I don't find any documentation on how to add the authentication to Graph at the same time as the already existing authentication to my website.
You could follow this tutorial about using OpenID Connect middleware and the Active Directory Authentication Library (ADAL) for AD v1.0 endpoint.
Note: You need to set the required permissions for your AAD app to access Microsoft Graph API on Azure Portal,then change the GraphResourceId under appsettings.json
to https://graph.microsoft.com/, and change the related request endpoint and parameters for accessing user profile under UserProfileController.cs.
Also, you could follow Microsoft Graph Connect Sample for ASP.NET Core 2.0 for Azure AD v2.0 endpoint.
Additionally, you could leverage the built-in Authentication and authorization in Azure App Service and follow Configure your App Service app to use Azure Active Directory login without manually add authentication middleware in your code. Then you could retrieve tokens in your app code, details you could follow here.