Ambiguity in the Definition of Resonance Frequency
Write differential equations that describe a circuit. Set all sources equal to zero. Find the non-zero functions of time that satisfy the differential equations.  For lumped, linear, time invariant circuits, these functions will be complex exponentials. A “resonant frequency” in radians per second is the imaginary part of the argument of the complex exponential. This definition works for all circuits, as well as lumped mechanical systems.

The resonant frequencies are a property of the circuit, and have nothing to do with inputs or outputs.