I just ordered the battery model specified. When it arrived, I realized it doesn’t have the same specs as the battery that comes with the thermostat.
The part listed (TL284443) is 3.7 VDC, but it is only is 380mAh (1.41 Wh) (if you zoom in on the image when you click “Buy”, you can see)
You can clearly see in the tear-down that the battery that comes with the thermostat is 2.1 Wh.
It might work as a replacement, but doesn’t have the same capacity.