I have changed my router with another one. How to integrate back my devices into the new router and network?

You can use the Shelly App feature "Wi-Fi batch change" to transfer your device to a new network. However, to do this you still need to have the old SSID available. Another option is to use the old SSID name and password for the new router. Otherwise, you must factory reset each unit and add it again with the new SSID.