Google Nest does not make it easy to change Wi-Fi settings on most of its devices, so its first recommendation is "to update your home network so that the network name (SSID) and password are the same as before. This will usually work even if you’ve purchased a new Wi-Fi router as long as the manufacturer settings are the same." We did that when we changed our Wi-Fi router/modem, and did not have to make any changes to our Google Nest devices.
If you can't manage that, then Google Nest's process is to remove your Google Nest devices from the Google Nest app or Google Home app while you are still on your old Wi-Fi network, then perform a factory reset, and then re-install the devices on your new Wi-Fi network.
If you miss the first step, you may have problems that will require assistance from Google Nest Support to resolve.