I added WiFi to my fridge and it's pretty great. It will tell me when the door is left ajar or when the temperature goes too high or low in either the fridge or freezer compartment.
However I made it myself with an ESP8266 and some Dallas sensors. So it only works for me. Not for anyone else.
I use the WeMos D1 Mini. It's a small board with fewer pins than a NodeMCU or Lolin D32 board but more than sufficient for stuff like this. The ESP32 is more powerful but to be honest for a simple bunch of wifi sensors it's overkill. Though one thing that is nice is that the ESP32 has a dual-core CPU meaning the WiFi can run on the second core. It's more responsive as a result but again, for this kind of stuff it doesn't really matter. You can find WeMos (or knockoffs which work fine) for 2$ everywhere.
The ESP32 also has bluetooth which the 8266 doesn't. But WiFi and BT can't be used at the same time, you can turn them both on but they have to share the 'airtime' meaning more airtime for BT is more packet loss for wifi. If I need both I will usually just use 2 for this reason :)
For programming I used https://ESPHome.io which is perfect for Home Assistant and you can program it right from the Home Assistant interface, just by declaring a few variables. I even have a $2 OLED display hooked up to it (SSD1306 1-color typical aliexpress thingy), works perfectly.
It's highly recommended, let me know if you have more questions.
And yeah like the other person said, power supply for these boards is irrelevant, any USB supply will do. They're not fussy because they don't use a lot of power unlike a pi.
However I made it myself with an ESP8266 and some Dallas sensors. So it only works for me. Not for anyone else.