First, know that 2.4GHz and 5GHz are frequency bands. There is much more to the differences between 2.4GHz and 5GHz besides speed. 2.4GHz has longer range, requires less power, and is older WiFi band. Many low cost, low power devices, such as thermostats, only operate on the 2.4GHz band.
There is no reason to replace your thermostat, you just need to figure out how to get it connected to the G3100.
While I don’t have a G3100, I do know it likely starts up with the Self Organizing Network (SON) feature turned on. When this is turned on, a single WiFi network appears that covers both the 2.4GHz and 5GHz bands. The router detects which band provides the best signal for a device and steers it to that band. This works well for some dual-band devices to ensure they get the strongest and fastest signal as they move around. However, some older devices many not work well with SON. In that case, it’s best to turn it off and go back to two different networks for each band and let the device pick which to use.
You should be able to check the status of SON from the MyFiOS app or from the router’s web page. If you find it’s turned on, try turning it off and then configure two different names for the 2.4GHz and 5GHz bands. Then, point your thermostat at the 2.4GHz band.