Does this violate the “Dependency Inversion Principle”?

Ideally you would inject the factory into the TestConnection (i.e. It would take a ConnectionFactory as a parameter, by an interface) rather than calling "new" to get a factory. That way the TestConnection doesn't depend either on the concrete implementation of the Factory or of the Connection.

While it can be argued that your general architecture is not the best way to go about implementing database connections, I'll skip that as I understand the question to be more about Dependency Inversion rather than database implementation. To achieve full Dependency Inversion.

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