Well, simply... software component that combines visual elements, like windows, graphics, and text, into a single image on a screen. X11 is the old compositor and Wayland is the new Linux standard. So its handling the on screen display of things.
The Desktop Environment (DE) is graphical user interface (GUI) elements such as icons, toolbars, wallpapers, and desktop widgets, i.e. its the GUI. Some of these ahve built in compositors.
I'm a KDE guy so in OpenSuse Tumbleweed I am at KDE Plasma 6 (the DE) and Wayland (the compositor).
I don't know what the Bookworm versions of these pieces are but from what I was able to see it may be behind the curve with the current leading edge of where the current versions of some of these apps are at. I know a year ago (is Bookworm that far behind compared to Tumbleweed, I don't know?) Wayland was pretty flaky.
So start with the DE. What is your preferred DE and why? (Because Debian/Ubuntu uses it is not the best answer ;) Decide on the DE and then the compositor will fall into place. Wayland is the future in compositors for Linux and it's solid on Tumbleweed, but this is with the latest versions of all of these components. The old X11 compositor is going away.
Conky is not all that Wayland friendly I hear. I still love Gkrellm and use that. This might shed some light on Conky and give you some ideas:
But the fix might be up to the Conky devels or be using a later version (latest) of Conky. What version is that you are using and on what DE and what compositor?
Let us know if you have questions...
Rick Kunath, K9AO
