Note that, apps in the same App Service plan share the same compute resources. To determine whether the new app has the necessary resources, you need to understand the capacity of the existing App Service plan, and the expected load for the new app. Overloading an App Service plan can potentially cause downtime for your new and existing apps. Refer App Service limits for more details.
As specified in the documentation, isolate your app into a new App Service plan when:
-The app is resource-intensive.
-You want to scale the app independently from the other apps the existing plan.
-The app needs resource in a different geographical region.
If your process is running slower than expected, or the latency of HTTP requests are higher than normal and the CPU usage of the process is also high, you can remotely profile your process and get the CPU sampling call stacks to analyze the process activity and code hot paths. Refer Remote Profiling support in Azure App Service for more details.
Hope this helps.