> Still when I ask Claude.AI to double-check the math on our power consumption, it thinks we have an incredibly leaky apartment. Like ridiculously off the charts. This also lines up with my inability to run a humidifier in the winter. I got the biggest, baddest humidifier I could find, and it barely makes a difference.

I would have started figuring this out before spending any money on a mini-split. OP, your climate envelope has failed somewhere. Spend some more money on a IR camera and try and identify where that leak is. Your basically just air-conditioning some of your apartment and some of the outdoors.