[fix] Stabilize MPI tests and prevent hangs #4256

Job	Run time
pre-commit / pre-commit	1m 7s
ubuntu / clang-build (ubuntu-24.04-arm)	2m 9s
ubuntu / gcc-build (ubuntu-24.04, Release)	2m 28s
mac / clang-build (Release)	2m 51s
ubuntu / gcc-build (ubuntu-24.04, Debug)	2m 34s
ubuntu / gcc-build (ubuntu-24.04-arm, Debug)	1m 46s
mac / clang-build (Debug)	3m 19s
ubuntu / gcc-build (ubuntu-24.04-arm, Release)	2m 13s
ubuntu / clang-build (ubuntu-24.04)	2m 40s
windows / msvc-build (Debug)	3m 33s
windows / clang-build	4m 3s
windows / msvc-build (Release)	3m 58s
ubuntu / gcc-test (ubuntu-24.04-arm)	8m 21s
ubuntu / gcc-test (ubuntu-24.04)	8m 49s
ubuntu / clang-test (ubuntu-24.04-arm)	8m 28s
ubuntu / clang-sanitizer-build (ubuntu-24.04)	3m 26s
ubuntu / clang-test (ubuntu-24.04)	8m 25s
mac / clang-test	4m 59s
windows / msvc-test	5m 20s
windows / clang-test	3m 14s
ubuntu / clang-sanitizer-test (ubuntu-24.04)	3m 3s
windows / clang-test-extended	2m 58s
mac / clang-test-extended	3m 18s
ubuntu / clang-sanitizer-test-extended (ubuntu-24.04)	2m 38s
windows / msvc-test-extended	2m 52s
ubuntu / clang-test-extended (ubuntu-24.04-arm)	4m 34s
ubuntu / clang-test-extended (ubuntu-24.04)	4m 32s
ubuntu / gcc-test-extended (ubuntu-24.04-arm)	4m 40s
ubuntu / gcc-test-extended (ubuntu-24.04)	4m 34s
ubuntu / gcc-build-codecov	7m 24s
perf / ubuntu-gcc-build-perf-stats	1m 34s
perf / macos-clang-build-perf-stats	1m 55s
pages / build-doxygen-xml	1m 41s
pages / build-scoreboard	17s
pages / build-sphinx	56s
pages / deploy-pages	0s
	2h 10m 39s

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