Thanks folks! I think you're right on the money about the doorbell. I took the button off once to see if I could re-route it for a Ring bell (my doorbell is on the side, unfortunately), and I seem to recall seeing what looked like cat5 connected to it. I looked a little closer last night and I actually think it's Cat3.

So that makes sense. I suspect that the wire going out to the right goes the button and the wire going to the left goes to the actual bell.

I know it's not to my humidifier. I just rewired that today so that it's controlled by my Ecobee instead of the humidistat in the duct, and that's powered through the C terminal on the furnace control panel.

Thanks for solving my mystery!

***edit***

Wow, Google autocompleted a search about moving my doorbell to the front, and there's tons of people looking for advice on how to move it, specifically for a Ring doorbell. Funny. Hopefully someone will have a suggestion similar to my setup...