[Solved] WiFi Socket Model for Local Control Without Internet Access?

Are there, and what is the name of the model of WiFi socket that I could manage via WiFi (turn on/off) also when there is no Internet (when there is an interruption of Internet supply to the router). At the moment I have a GoSund socket (Smart WiFi SP111 3680W 16A Tuya) and I have connected an "external" Horizon router to it (from UPC cable) and sometimes I would like to turn this Horizon off and on, but when I turn it off there is an internet outage and the Android app for the socket stops working at all and I have no way to turn the socket on remotely. The wifi is from a router connected "downstream" to the Horizon ("cascading" NAT). So I have WiFi all the time (Intranet) but Internet not necessarily.
In general, the idea is that I can *remotely* turn the Horizon router off and on because sometimes the quality of the Internet connection drops. I can't find a function to reboot in the Horizon's web menu. Horizon is about 2 walls away from me

gosund.gif Download (93.96 kB).

Search:
Compatibility with Tuya Smart Life allows Wifi-compatible devices communicating over Wifi to be connected to ZigBee devices and create interdependencies, but please note, that without internet access only sensors and relays communicating using the ZigBee standard will work.

Maybe a remote control socket, just curious if it will 'reach' through those 2 walls.

And what does "remotely" mean? Completely from outside the house or remotely from another room? Because if the latter, there are radio sockets controlled by remote control.

They exist, or rather they can exist. There are several ways:
If the socket has a wifi ESP chip - upload Tasmot.
If the socket has a wifi Beken chip - upload Openbeken.
It is possible to make such a socket yourself using the above mentioned ways.
For example, buy a relay, a mini inverter for 3.3V and esp8266 e.g. version esp01 and use the housing from the time controller.
Nevertheless it is not worth it, because for about 12pln you can buy a ready-made Tuya smartplug to upload Openbeken, because recently only these chips are mounted in them.

The Tuya WiFi devices are operational if the router (local network) is on, even without internet access (e.g. WAN cable disconnected). They can be switched on and off from the app. Scenes, on the other hand, do not work.

A socket with Tasmota software uploaded solves the problem.