If you have factory reset the Play:3 and setup that with a reset App you have ‘likely’ split your Sonos system into two. I would now wire the Sonos One instead and temporarily power off the Play:3
Reset just the Sonos App and connect back to the ‘existing’ Sonos system stored on the Sonos One.
Only when you have that Sonos One speaker up and running in the App, factory reset the Play:3 and add it to your system using “Settings/System/Add Product” and follow the on-screen instructions.
When complete, just check you have the new ISP routers WiFi credentials stored in your Sonos App network settings. If not, then follow the instructions in the link below to add them to your Play:3 - note you may need to remove the old WiFi credentials from your Sonos system too, so I’ve included a further link that should lead you through that process aswell…
https://support.sonos.com/en-us/article/connect-sonos-to-a-new-router-or-wi-fi-network
https://support.sonos.com/en-us/article/remove-a-wifi-network-from-your-sonos-system
Once you have both speakers up and running with the correct WiFi credentials showing in the App, you can then uncable the Sonos One and move it back to where you want it and run both on your WiFi network.
Hope that assists.