Good day@ClearIdiot, sorry to hear that you've had a hard time setting up the plug, sometimes it may stuck at certain set up, I wish I could do some help:

It seems that  Kasa APP could not find smart device , you could try some suggestions here and see if that helps: 

• Make sure phone is connected to the default SSID ' TP-LINK_Smart _XXXX' in set up process or smart device could not be found by Kasa APP. 

(the defalt SSID has no Internet and it will disappear after smart device is installed successfully. )

• Turn off VPN settings on your phone 
• Try to turn off the mobile data
• Manually Connect to TPLINK _ Smart XXX SSID when the app guides to connect to smart Wi-Fi, and go back to Kasa app

iOS: Go to the Settings page, click on the Wi-Fi option to connect to the Kasa Cam’s Wi-Fi manually.

Android: Go to the Settings page to connect to the Kasa Cam’s Wi-Fi network. Once it’s connected, please go back to the Kasa app and click on "Try Again".)

•  for IOS14 and above, enable Local network Permission for Kasa app 

https://www.tp-link.com/support/faq/2937/

• Try a different phone

Hope this could help, if still no luck may I have a photo of the error message on app, thank you.