fix: Mingw64 corrected and add a CI job to test it (#3132)

* mingw64 platform string is like mingw_xxx not "mingw"

See https://github.com/msys2/MINGW-packages/blob/master/mingw-w64-python/0099-Change-the-get_platform-method-in-sysconfig-and-dist.patch

* Mingw: Do not dllexport exceptions

This is a fix for errors like:

D:/a/pybind11/pybind11/include/pybind11/detail/common.h:735:23: error: 'dllexport' implies default visibility, but 'class pybind11::builtin_exception' has already been declared with a different visibility
  735 | class PYBIND11_EXPORT builtin_exception : public std::runtime_error {
      |                       ^~~~~~~~~~~~~~~~~

* GHA: Test Mingw64 build

* fix: avoid thin binaries on mingw

* fix: drop lto on MinGW

* Mingw64: disable PYBIND11_DEPRECATED

It trigger many warnings for unknown reasons

Co-authored-by: Henry Schreiner <henryschreineriii@gmail.com>

.github/workflows/ci.yml

@@ -859,3 +859,34 @@ jobs:
 
     - name: Run all checks
       run: cmake --build build -t check
+
+  mingw:
+    runs-on: windows-latest
+    defaults:
+      run:
+        shell: msys2 {0}
+    steps:
+    - uses: msys2/setup-msys2@v2
+      with:
+        install: >-
+          mingw-w64-x86_64-gcc
+          mingw-w64-x86_64-python-pip
+          mingw-w64-x86_64-cmake
+          mingw-w64-x86_64-make
+          mingw-w64-x86_64-python-pytest
+          mingw-w64-x86_64-eigen3
+          mingw-w64-x86_64-boost
+          mingw-w64-x86_64-catch
+
+    - uses: actions/checkout@v1
+
+    - name: Configure
+      # LTO leads to many undefined reference like
+      # `pybind11::detail::function_call::function_call(pybind11::detail::function_call&&)
+      run: cmake -G "MinGW Makefiles" -S . -B build
+
+    - name: Build
+      run: cmake --build build -j 2
+
+    - name: Python tests
+      run: cmake --build build --target pytest