We have an app deployed in Azure App Service, and it has the below logging configuration:
If we are not using any methods in the System.Diagnostics namespace (System.Diagnostics.Trace / System.Diagnostics.TraceSource), then what is the relevance of this setting? We have noticed that the system performs poorly when the level is set to "Verbose" and the performance improves when the level is set to "Warning". However, we do not have code that uses
System.Diagnostics.Trace.TraceInformation or System.Diagnostics.Trace.WriteLine
to write a trace.

Keep in mind your code is not the only thing that executes when a request comes in.
Even if you are not using the System.Diagnostics.Trace namespace in your application, chances are you have some NuGet packages or other dependencies that might be.
In addition to this, the server code that hosts your app takes this input as a flag to spin up the necessary process to listen for and capture trace events and this in itself competes for resources with your app.
You should check the output file in your blob storage to get an idea of how much data the verbose level generates.
You should not set the logging to verbose unless you are tying to collect information to diagnose an issue. For production workloads you would generally want to set this to errors only.