To host multiple apps under a single domain, if you’re leveraging Azure Web App and deploy your web applications to each virtual directory with the name which could identify your web application.
You could keep your web sites in separate projects and use the ‘virtual directories and applications’ settings in Azure to publish the two different projects under the same site.
Go to WebApp -> Settings -> Application Settings -> Virtual applications and directories.
In Web Apps, each site and its child applications run in the same application pool. If your site has multiple child applications utilizing multiple application pools, consolidate them to a single application pool with common settings or migrate each application to a separate web app.
You may want to check the blog post Deploying multiple virtual directories to a single Azure Website for more details.
Also, you could also use Application Gateway infront of your app since you can do path based routing with app gateway i.e testing.com/one points to one web app and testing.com/another points to the other app. You could start out with the example below the modify the back end to use path-based routing. Kindly refer the links below one that covers the basics of configuring the App Gateway with a WebApp and one discussing path based routing:
https://blogs.msdn.microsoft.com/waws/2017/11/21/setting-up-application-gateway-with-an-app-service-that-uses-azure-active-directory-authentication/
https://learn.microsoft.com/en-us/azure/application-gateway/application-gateway-create-url-route-portal#create-a-path-based-routing-rule