My ductless house has a gas combi water heater/boiler and hot water circulation system to in-wall radiators with simple blower fans.

The house also has an exhaust fan on a timer, paired with small vents on several windows around the house, to cycle in fresh outside air. But practically for much of the year we just open the windows for fresh air since we live in the temperate PNW climate, wildfires aside :(

I looked in to installing a minisplit heat pump system last year, but the quotes I got were outrageous ($25k+) plus as a retrofit it's not the most elegant integration. Someday I'd like to do the conversion and ultimately decommission the gas boiler, but at that price tag it's not happening soon.

In the short term I bought one window AC and one portable AC for a combined ~$1000. It's not ideal but we only have a few weeks a year where cooling is really needed, and a few more where it's a nice luxury but not a necessity.

"Ductless homes" usually circulate hot water through radiators. If you switch to a heat pump, nothing's stopping you from circulating cold water in the summer, though obviously there is a limit on the temperature delta (you can heat water much more than you can cool it). Bringing in fresh air is a manual process (open the windows), and filtering air or controling humidity is then left to seperate appliances, if done at all. Though small fans to the outside for forced ventilation are gaining some popularity for giving you automatic air exchange and filtration.

Maybe a faulty assumption; my AC-less home has a ducted oil furnace, and we still haven't removed the ducts after installing a heat pump. Another house I lived in 12 years ago had ducts for oil furnace heating but no AC. Both were 100+ years old and in the northern US.