GH-49948: [CI][C++] Revert PR 49931 (Pin MinGW MSYS2 packages) but keep bumped minIO version

[tadeja]

Rationale for this change

Ready to revert pinned packages on MINGW64 with tests all passing now - see updated umbrella issue #49948 and #49958.
Past origin PR discussion #49931 (review)

What changes are included in this PR?

Reverting PR #49931's temporary pins workaround - so completely removing step - name: Setup MSYS2.

Are these changes tested?

Yes, tests now pass on current upstream MSYS2

Are there any user-facing changes?

No.

• GitHub Issue: [C++][CI] gcc-16 MinGW failures - remaining fixes (follow-up to #49930) #49948

[github-actions]

⚠️ GitHub issue #49948 has been automatically assigned in GitHub to PR creator.

[tadeja]

See updated #49948 and #49958, ready to revert pinned package versions with this PR!

GCC 125312 related fix already merged in upstream MSYS2 - Version 16.1.0-4 is available on https://packages.msys2.org/packages/mingw-w64-x86_64-gcc-libs, it downloads and allows all tests on our MinGW job to pass now:
https://github.com/apache/arrow/actions/runs/25937291262/job/76296127141#step:5:109

[rok]

I've followed the upstream development and this makes sense to me. Will merge if CI green.

[raulcd]

This is great! Thanks @tadeja

[conbench-apache-arrow]

After merging your PR, Conbench analyzed the 4 benchmarking runs that have been run so far on merge-commit 27513af.

There was 1 benchmark result with an error:

• Commit Run on amd64-m5-4xlarge-linux at 2026-05-16 14:24:02Z
  • dataframe-to-table (Python) with dataset=type_dict

There were no benchmark performance regressions. 🎉

The full Conbench report has more details. It also includes information about 3 possible false positives for unstable benchmarks that are known to sometimes produce them.