MSYS2 is repacked Cygwin though. It is literally the same codebase compiled with slightly different flags. You need a full Unix environment for Bash to run, not just Mingw toolchain. The difference is Cygwin aims to create a full Unix system while MSYS2 just enough development environment to run bash, make etc to build native Windows programs with Mingw.

Git installs its own Mingw and Msys2 stuff but mostly compiled for a Mingw environment so they consume Windows paths natively instead of using MSYS2/Cygwin path conversion. That's why when you have mixed PATH variable all hell breaks loose with Git.