Maybe not as fun but my sun room window unit is controlled by an off the shelf $20 thermostat designed for Air Conditioners. It’s the LUX Win 100 and is date/time programmable and features a compressor lockout so it doesn’t burn out your window unit by short cycling.

If you have a favorite smart thermostat you could also wire up a receptacle with a contactor between it and a cord and a 24v AC transformer wired to the line side. This would make your window unit controllable just like a central air conditioner.