Are you using the linked code exactly as it is in the example (with the addition of SSID, Password and Auth Code of course) or have you made any changes?
The code won’t work for the Uno as it stands, as you’ll see from the comments in the code.
Please post your EXACT code, minus your credentials.
ETA, having looked at your wiring in more detail, it seems that you are using the UNOs Rx and Tx pins, which you can’t do with this code example. See this explanation of why: