Impedance isn't meaningful with an active BT headphone. It's 1,530Ω on the Bathys, but that's just the input impedance of the amp in the headphone. Very high impedance is normal in this case, it would be the same as measuring the impedance of the RCA input on an amp.

An incoming analog 3.5mm signal is digitized, the ANC and any other DSP performed, and it's fed through the internal DAC and amp at that point. The 3.5mm input takes a line level input, it doesn't need external amplification, that's in the headphone. Best quality, you'll get keeping it digital and using the USB C input rather than the 3.5mm, that is just there for compatibility/convenience, such as if you want to plug it into an in-flight entertainment system.