Allow MLFlowLogger to work with mlflow-skinny

[dconathan]

What does this PR do?

mlflow-skinny is a variant of the mlflow library that installs the bare-minimum required for tracking: https://pypi.org/project/mlflow-skinny/

Even though this should be enough to enable the MLFlowLogger, it doesn't work because:

https://github.com/Lightning-AI/lightning/blob/4a802e00a843264afd5aea023d8475d4f1b4d360/src/pytorch_lightning/loggers/mlflow.py#L40

checks that precisely the mlflow library is installed.

This PR looses the restriction to check for the mlflow-skinny library too.

Fixes #16486

Does your PR introduce any breaking changes? If yes, please list them.

If there are users that have the mlflow-skinny library installed and are counting on the MLFlowLogger not working, but I can't see why that would be the case...

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[dconathan]

@carmocca do we currently test in an environment where mlflow is installed? I see the logger is tested here https://github.com/Lightning-AI/lightning/blob/master/tests/tests_pytorch/loggers/test_mlflow.py but I don't see where to make a new environment to run the tests with mlflow-skinny...

[carmocca]

@dconathan We don't install the logger libraries in our CI and instead mock them entirely. This PR could be merged as is as long as the tests pass.

Can you also add this change to the CHANGELOG?