Metal-CPP is a header only Library which directly calls into the Objective-C API. So it will support any version of Metal, including Big Sur.
However the latest version may have newer symbols that did not exist on older Ones. So if you used those, you will get API validation or unrecognized selector errors at runtime. If you see such errors you will need to check the documentation or Objective-C headers to determine when the symbol was added. This is a problem that is less likely to occur if using the Objective-C API, because availability macros would warn you of such errors at compile time.