configure: Check for valid Python on MinGW as well

The LLVM build system is somewhat picky about which Python is used to build it
as it's known to be incompatible with the default `python2` package that ships
with MinGW. This was previously detected for MSVC builds but the logic was left
out for MinGW by accident (now that we've switched to cmake builds for LLVM
everywhere).

This corrects the `./configure` check and also updates the `README.md`
accordingly. Additionally, a number of instructions were updated to work with
the most recent copy of MSYS2.

Closes #34489

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