I don't believe X11 provides any means for Clients to ask the server for any information about any window

Sure it does. Ever used xmag? Or a graphics editor like xpaint that allows you to pick the colour of any pixel on the screen? xli or xloadimage, that can inspect or share colour palettes already in use (important in the time X-servers often used 256 colour palettes)? fvwm2 has no problem using partially transparent icons; and if I view a partially transparent gif with display (which comes with ImageMagick), I get to see what's underneath (and even the focus goes to the underlaying application). And you may be familiar with xscreensaver which has a few screensavers that use the current display.

You can say a lot of bad things about X, that it's slow, that it uses a lot of memory, that it's insecure, and that it's hard to program with. But the one reason that it's still going strong is that anything is possible. And that includes transparency, and inspecting the pixels of other applications. But I'm not an X-windows programmer (it's been more than 10 years since I last wrote an X-windows program (in C, pure, raw X-windows, no widget sets used)), so how it's done, I do not know.

Abigail