It sounds like you shouldn’t be using that site. Anyway Ublock origin is a must now.

windows does not have any built in way to take screenshots with the mouse cursor

Whilst this comment isn’t really related to the popup itself, why couldn’t you use the native screenshot capability (e.g. Snipping Tool)? It’s entirely navigable by mouse cursor if you want, and available to every Win10/11 user. I’m not sure what other type of problem / limitation you’re trying to describe here…

Window key-shift-S;

Try the rectangle select option. You can also set options to include the mouse, etc, after a delay

I forget the key combo…

alt + PrtScrn

or

ctrl + PrtScreen

Open up your image app, paste from clipboard. file - save as… bingo, “built in screen shot”.

one of the shortcuts does “current active window” and one does the whole display.

Windows has a built-in screenshot tool that’s already been mentioned, but I’ve been using Greenshot for a while and it works well. Print Screen button as a shortcut and it freezes the screen while you draw a rectangle to screenshot, so if you want the mouse pointer in the shot you just put it in the right spot and hit Print Screen.

The irony of buying a paper version of a book about pdfs really gets me

?? why not click the X ?

There’s Greenshot.

Overlaying the button with another ad is another good strategy.

It’s time for you start to using LibreWolf (uBlock Origin pre-installed)

Time to Linux :D