Is there any compatibility matrix as to what Visual Studio Versions (Say, ranging 2005 - 2017) are compatible with which Windows SDK Versions?

There's "A Brief History of Windows SDKs" article exists, which contains such a table. It's written by @chuck-walbourn, a Microsoft employee. Although being initially posted in 2013, it appears to be still updating, as it mentions Visual Studio 2022. Unfortunately, it doesn't feel truly complete, and I wouldn't consider it official. For example, it doesn't mention "Windows SDK 7.1A for v141_xp Platform Toolset" for VS 2019, which is not only usable there, but is also available for it directly from the Visual Studio Installer, under the name "C++ Windows XP Support for VS 2017 (v141) tools [Deprecated]".

Should any Windows SDK be fully compatible with "any" C++ compiler, or are the different Windows SDK versions bound to certain compiler versions?

Seems to be the case since VS 2015. Of course, this only applies to compatibility between new Visual Studio editions and preceding SDKs, not the other way around.