When you get a new router the easiest way to get everything back online quickly is to reset the new router to exactly the same SSID and Password as the old one. Then, when it reboots, all your devices will never know there is a new router and log right back in.
Unfortunately, because you have already done a reset on the T-stat, that is a moot point because it has to be reinstalled.
You are also experiencing a thermostat stuck in it’s setup routine which is difficult to get out of. There have been successful attempts to get thru that though. The last user I helped placed their phone in Airplane mode to shut off the WiFi and the Cellular Data on their phone before attempting to delete the device and then enabling the internet after it was deleted. This cuts the Wyze server out if the decision making process. This may work for you.
After that, you should be able to run a setup with the wires you have already connected.