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

> ### `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

https://github.com/Azure/azure-cli/blob/71ab97d61b4b70d2d37f5e3e465a16dbde37c1e8/src/azure-cli-core/azure/cli/core/commands/client_factory.py#L145

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**