I love heat pumps, but the author should have had an energy audit done first. Likely a thermal camera on a cold day would quickly identify their envelope issues.

> one from the clothes dryer (when I hold an incense stick up to it I can see it pulling in air even when it’s not running)

A normal vented clothes dryer can vent something like 8000 cu ft of air in a normal drying cycle (i.e. all of the air in their apartment). If that's running all the time somehow, that could definitely explain a lot. If that's the case they should fix it, and maybe explore ventless heatpump dryers.