What version of the transport are you using? Based on the version, the connection string would be different.
Endpoint=sb://[NAMESPACE].servicebus.windows.net/;Authentication=ManagedIdentity was a workaround for the ASB SDK track 1. Track 2, the latest ASB SDK/NServiceBus transport, the workaround was removed by the SDK team in favour of a more consistent approach, which only requires the fully qualified domain name (FQDN) for your namespace as a connection string. Try [MYNAMESPACE].servicebus.windows.net as your connection string with Managed Identity configured application/environment. Here’s an example of Azure Functions using MI and here’s the documentation for WebJobs, the guts of Functions.
PS: this was the blog post where the SDK team has shared all the options to configure Functions extensions using Secretless configuration. Same time of configuration is likely to be applicable to App Service as well.