Do install msys2 in CI

.github/workflows/ci.yml

@@ -62,6 +62,9 @@ jobs:
     name: ${{ matrix.full_name }}
     needs: [ calculate_matrix ]
     runs-on: "${{ matrix.os }}"
+    defaults:
+      run:
+        shell: ${{ contains(matrix.os, 'windows') && 'msys2 {0}' || 'bash' }}
     timeout-minutes: 360
     env:
       CI_JOB_NAME: ${{ matrix.name }}
@@ -77,6 +80,26 @@ jobs:
         # Check the `calculate_matrix` job to see how is the matrix defined.
         include: ${{ fromJSON(needs.calculate_matrix.outputs.jobs) }}
     steps:
+      - if: contains(matrix.os, 'windows')
+        uses: msys2/[email protected]
+        with:
+          # FIXME(#136795): this mingw installation seems to be needed for
+          # `i686-pc-windows-gnu`, otherwise we somehow incorrectly ship the
+          # 64-bit `libwinpthread-1.dll` and then `rustc` explodes.
+          #
+          # i686 jobs use mingw32. x86_64 and cross-compile jobs use mingw64.
+          msystem: ${{ contains(matrix.name, 'i686') && 'mingw32' || 'mingw64' }}
+          # don't try to download updates for already installed packages
+          update: false
+          # don't try to use the msys that comes built-in to the github runner,
+          # so we can control what is installed (i.e. not python)
+          release: true
+          # Inherit the full path from the Windows environment, with MSYS2's */bin/
+          # dirs placed in front. This lets us run Windows-native Python etc.
+          path-type: inherit
+          install: >
+            make
+
       - name: disable git crlf conversion
         run: git config --global core.autocrlf false