I wonder if there is a way to access the current logging level of a connector in Mule 4.
e.g., I have configured an Logger:
Is there a way to get the level configured for it?
You are confusing "connector properties" with logging configuration. Don't try to access directly to information you see in the debugger. That's just not how it works and it is undocumented at best.
The logging configuration is not a connector configuration but a per Java class property. I don't believe it available for easy retrieval from a flow.