I use the Kinsa thermostat and like it. I see your point about having to have it plugged into the phone, but it hasn’t been an issue for me.
The Kinsa app writes it’s data to Healthkit, which is important for me because I can then export it using the QS Access app.
I find it interesting that the device has a long reading mode. This takes, maybe, three minutes to complete. I assume that this will give you a more accurate reading, though it makes me wonder what shortcuts or assumptions the short reading mode is making. And if there are similar issues with other thermostats.
In terms of getting data out, if you have an iPhone, you may want to get into the habit of manually entering your data into the Health app whenever you take a measurement. I measure my blood oxygen level at the same time as I take my temperature and I have to manually enter it that way.
I haven’t tried any other smart thermostats.