We have a similar problem. Despite having deployed the Dynatrace Extension successfully on the Azure App Service, the OneAgent (IIS) component is loading but the OneAgent (DotNet) component is not . The app was stopped and started as well. (Repeated uninstall and install, stopped and started several times).
As described above, we only see the Web Service calls, with no visibility into the transactions, e.g. database calls. Would be really helpful to understand if anyone has seen similar difficulties, and how to resolve.