That’s generally true for most HVAC applications. Bang-bang control creates limit cycle behaviour and as long as a small oscillation in temperature is acceptable, it’s a nice simple solution.

OPs problem seems to be a discontinuity between the two limit cycles, heating and cooling. The way to tackle this is to make time series vectors of all measurements and compare them with the subjective sensation of the room temperature. That should inform the relevant set points for the control actions.