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

You can use the Shelly Smart Control APP  feature "Wi-Fi batch change" to transfer your device to a new network. To access it, go to My Home -> All Devices and then click the icon at top right corner:

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.