An esp32 of your choice with a dht22 connected, running ESPhome. $5 should cover it id you have an old cellphone charger laying around. More if you need to use POW.
True but I included ethernet with wifi because wifi is ethernet, and wifi was not specifically mentioned, but as I said more than $5 if you want POE (…or other wired ethernet…)
I have several ESPhome bluetooth proxies and they all have a dht22 hanging off of them.
Altough it’s against all you wanted, i’ll still recommend you This xiaomi thermometer/hygrometer. It has BLE connection, but perhaps zigbee version can also be found (do some searching…)
CR2032, replaced once a year or so, extremly accurate, small, cheap (you can find it even cheaper that the one on above link), you don’t need to draw any wires, just position it anywhere you want…
I replaced all my thermo’s with these little models. I have three BT proxies around my house and that’s all i need. Just replace fw with pvvx and you’re done.