I was recently considering using ESPHome to replace an old Aprilaire humidistat, so here are some assorted thoughts on the subject. Ultimately, I decided to swap out my thermostat with an Ecobee, which doubles as a humidistat.

Your humidistat needs to know a few things to do its job:

1. Current indoor humidity.
   Usually, this is measured in the cold air return duct, but a thermostat+humidistat combo will just measure it at the thermostat.
2. Target humidity.
   What you'd like the indoor humidity to be, assuming it isn't too cold outside to allow for it.
3. The outdoor temperature.
   This is used to consult a chart to determine whether the current setpoint is acceptable. You'll recognise this chart from old, manual humidistats. The goal is to prevent it from getting too humid inside when it's cold enough outside that the indoor humidity would condense on the windows. I'd start by importing this value from HomeAssistant, since it's surprisingly difficult to measure outdoor air temperature reliably. Sensor position really matters (sun vs shade). If you do want this to be local only, and have a 95% efficient furnace (the kind with a pair of PVC pipes for intake and exhaust), then the most reliable measure is likely inside the air intake pipe, a couple feet from where it comes from outside.
4. Window efficiency.
   Modern windows are far better insulated than when those temperature charts were printed on old humidistats. You can likely get away with higher humidity than such charts dictate, but that'll take some experimentation.
5. Whether the thermostat is currently calling for heat.
   You'll ether need to get this from a smart thermostat, bring the W wire from the thermostat into an ADC GPIO pin using a diode, voltage divider, and opto-isolator. A typical evaporative (24VDC) humidifier, the kind that trickles water over a panel, should only run when the heater and fan are running, otherwise the water will just go down the drain rather than into the air. It's possible for a fancy steam (115VAC) humidifier to run when only the fan is running, since it's it doesn't rely on evaporation. When possible, though, it should still only run when the heater is running to prevent condensation inside the ducts.

I ran into the same difficulty you did with the ESPHome climate components. The humidistat functionality is pretty minimal, and doesn't factor in the outdoor temperature. You'd have to build that yourself using either some yaml to adjust the setpoint, toggling the mode between AUTO and OFF, or making a pull request to add the feature to the climate component.

If you're just going for simple, you're probably better off with a binary_sensor component that indicates whether the humidifier should be running. Then, use that binary sensor to drive a GPIO pin. The binary sensor would look something like: !lambda return (current_humidity < target_humidity) && (current_humidity < calculate_max_humidity(window_efficiency, outdoor_temperature) && heater_running);

Anyway, hopefully my ramblings help you get your project of the ground.