It sounds like you have everything connected correctly. Your interface won’t output sound to the monitors unless you tell it to. You can do this in the interfaces bundled software, your DAW, or if running windows 10 with the right drivers from control panel
Yes plugging this audio into a mic level input that is pre-amped is no good.
Does your interface not an instrument input. May only be 1 jack input but it should be stereo. So it sounds like you need dial mono jack to single stereo jack.
Or.
You could tell us the interface you have?
I was actually doing that because it was louder, which my mind thought instantly that it was better. I have the Steinberg UR22 mkII, but I actually connect my DT (and my Volca Bass) to a mixer and from the mixer I was using the trs to xlr cables to my interface. But I actually have some guitar cables that I can use to connect it to the interface. It has this mixed mic/line inputs and it recognizes the signal depending on which cable you connect into it. So, from now on, using instrument cables