AZURE CLI should add extension name to UserAgent but it doesn't work

[xfz11]

az feedback auto-generates most of the information requested below, as of CLI version 2.0.62

Related command

This bug exists on every extension API request. Take containerapp extension as an example
az containerapp list

Describe the bug

This line show that CLI should add extension name in UA but it doesn't work

azure-cli/src/azure-cli-core/azure/cli/core/commands/client_factory.py

Line 145 in 71ab97d

client_kwargs['user_agent'] += "CliExtension/{}".format(command_ext_name)

The actual UA is 'User-Agent': 'python/3.8.8 (Windows-10-10.0.22621-SP0) AZURECLI/2.46.0 (PIP)' not extension information.

To Reproduce

Expected behavior

UA should contains extension name. Besides, we expect extension version is also added in the UA as CLI core version.

Environment summary

Additional context

[yonzhan]

route to CXP team

[xfz11]

route to CXP team

It should be a bug in Azure CLI core. az container is just an example. Every extension has the same issue.