@Cpmame,

The device should continue to work without an internet connection, it only needs its network connection to be alive. It is most likely that your phone is being seen as being on a different network, whether this is from a privacy setting such as Private MAC Addressing, Connected to a Different Mesh Node, or your phone could be defaulting to its cellular connection since your home wi-fi cannot provide internet at that time.

As the device is also a Matter plug, you are not tied to the Tapo platform. If you have another Matter controller on your local network, you can add the device to that hub - which would allow the hub to control the device over your local network, rather than through the internet. For your use case, I would highly recommend looking for another Matter platform you can add the device to - as some platforms may allow you to automatically reboot the plug when there is a detected internet outage.

For Bluetooth Control., a few years ago it was sort of determined at an industry level that Bluetooth is not an ideal method for controlling devices. Instead, Bluetooth was determined to be a better as a dedicated method of setting up devices. In fact, Matter devices require that this Bluetooth connection be used for device setup.  Last year, there were standards introduced that would allow for Bluetooth Control, and this technology is planned for our Atomlink series of devices releasing later this year.