Managed Services needs to remove that setting from Azure Portal
IIRC DXC-S will forcibly change the configuration to use trace logging to make logs available to epi for troubleshooting etc.
We've created a custom logger that writes to both Diagnostics Trace and Application Insights. But we couldn't register a custom logger factory because, as you said, Managed Services have added that Application Setting in Azure Portal.
So we created a support ticket to have it removed from all three environments, and it works fine now :)
Did anyone manage to override episerver:LoggerFactoryType in DXC-S?
I've registered a custom logger factory in the appSetting section of web.config and web.preproduction.config, but when I inspect ConfigurationManager.AppSettings in DXC-S, I still see EPiServer.Logging.TraceLoggerFactory, EPiServer.Framework.