Heater sometimes stuck blowing cold air on Auto

I have tried to find posts with this specific behavior but haven't found anything promising, yet.

2012 3rd Gen Prius with about 100,000 that I've had for almost two years. I have recently noticed that after turning on the heat (set to Auto with the temperature well above cabin temp, e.g. high or upper seventies) that cold air is blowing through the vents, e.g. feels like the A/C. It will continue unless I press the OFF button to turn off the climate control, and then begins working, e.g. blowing heat, after I turn it to ON again.

I usually notice this after starting the car and heading out, but I have also caught it doing the same thing even after I have been on the road but didn't turn on the climate control until later, e.g. the engine is definitely warm.

Prior behavior has always been that the climate control system would not turn on the blower fan unless there was warm air to dispense (after the engine has warmed enough). The heat works fine once I get it to engage. It's almost like it is frequently failing at first go, then works fine once I turn off climate control and turn it back on.

Any insight on what might be suspect appreciated.

Thanks!