Need Help Choosing Board

Hello all. I recently decided to embark on a brand new project, but first some monologuing. Our router constantly loses connection to the internet, the wi-fi is still up, but with no internet connection. My family typically restarts the router to remedy the situation, but I figured why not use an Arduino hooked up to a power switch tail. Looking at the variety of boards, I'm thinking the Arduino Uno Wifi Rev 3 fits the job, but I need to make sure that it is able to detect when the network loses internet connection in order to pull a pin high. Does this board have the capability to do so? And what would an example sketch look like, as I don't see any commands that would be able to scan a network or test to see if webpages (such as Google) are up? Along with posting here, I have also made a sister post in the programming forum, since the question is split 50/50. Thank you in advance, y'all really are a great community.