From some searching, it looks like the term you're looking for is an "auto changeover" thermostat. Honeywell is usually a pretty safe choice for thermostats and they have models with auto changeover. Some of those are technically 'smart' but can be programmed and operated without using the app.
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I'd also suggest checking for which models are eligible for energy rebates.
I can't imagine needing this. Its got to be crazy where you are. I mean if its been hot enough for ac to kick on it can get pretty cold outside my place and not get the indoor temp all that low. and vice versa.
That looks similar to my current model - look at the switch on the bottom:

It can be set to heat OR cool. Or neither. But not both. Apparently letting the internal thermometer decide if it needs hot or cool air is a tall order.
You’re right, the specs says auto but the instructions show is heat or cool only.
Here you go:
https://www.honeywellhome.com/products/t5-7-day-programmable-thermostat-1
Edit: there might be a cheaper one but you’ll need to look through the product catalog.
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