The Tuya integration is cloud dependent during operation. The integration class is “cloud push”.
LocalTuya is available via HACS, but is not “official” and may lack support for some devices. It works fine for some plugs I purchased early on, but that’s the extent of my experience.
Tuya devices aren’t designed to work purely locally, at least they need Internet connection when being set up. And honestly I don’t think there are many readily available pure-local(doesn’t need Internet at all) smart plugs on the market. TuyaConverter used to be a workaround, but Tuya enhanced the encryption and changed the chips to something else other than ESP8266, making them un-flashable.
That being said, I have 13 Tuya devices at home and they all work reliably in the past few month.