Subnetting the 5G Gateway

Assuming this means you set your Ring to a static IP, then you are correct. You need to reset or Ring to reconfigure it. The other possible solution is to add an external router for the 2.4 ghz band wifi and set that router’s IP to the same as what you had with the ATT router. I say “possible” because if you go with external router, then it will create two NAT layers for everything connected to the 2.4 ghz wifi. This may cause other issues or it may work just fine depending on what your connected devices and apps need.

Your extender won’t work because it doesn't support DHCP. It will still use the same IP range as the TMO router.

If you decide to give the external router a try, there are numerous posts in this community on recommended ones and how to connect to your TMO router plus disabling the wifi on some models of the TMO router.

If the expense is not palatable, you could always borrow an external router to connect to your Ring. Then you could change wifi setting via your Ring app. Just keep in mind that you can’t have both your TMO router and external router using the same SSIDs if both are turned on. You will have no control of which SSID your Ring decides to connect to if both are using the same SSID.