I would convert them over to esphome. Once they started locking them down I quit buying them.
IMHO the developers are waiting for tuya to do what all the others have and shut down the servers. Once that happens there will be around 29 percent of HomeAssistant users really angry.
I'm guessing a lot of people started off with tuya devices and then found HomeAssistant they continue to use them because they have them and they still work. It you are thinking about buying some reference my previous statement. It's not if but when they will stop the cloud servers.



No, zigbee devices no matter the brand don't need extra software because they use the zigbee communication protocol.
The Tuya software on HomeAssistant is used to bridge HomeAssistant to the tuya devices via the cloud generated keys if i remember correctly. The wifi tuya devices are the only one that utilize it and they still connect to tuya's cloud services.