Improve logging in autogen.oai

[sonichi]

Currently, the autogen.oai package has an experimental support for logging: https://microsoft.github.io/FLAML/docs/Use-Cases/Auto-Generation#logging-experimental
The data are logged in memory as a dictionary. This feature needs to be improved to persist the log automatically and support log analytics, and support #1063 .

Tasks

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1. Check whether the data format needs to be changed.
2. Choose a logging solution. For example, mlflow.
3. Write documentation and test.
4. Implement.
5. Write a notebook example.