TL;DR Sounds like a limitation.

I believe the doc's paragraph (https://docs.databricks.com/en/machine-learning/feature-store/python-api.html#limitations), "implicitly" but not very clearly, implies that a SparkSession with Access to UC and databricks resources is required; in case of DatabricksConnect it seems like it is not passed to the FEClient during initialization, otherwise it should avoid such Authorization errors.

I assume with this exception, you're also also finding a full stacktrace; you can confirm if the above is indeed the problem by inspecting it, and then identify which code line is raising the exception.