Harden MPI extension setup and docs #1735

Job	Run time
ci-scope	2s
pre-commit / pre-commit	2m 33s
pre-commit / link-check	-1s
ubuntu / gcc-build (ubuntu-26.04, Release)	2m 45s
windows / clang-build	2m 38s
mac / clang-build (Release)	2m 24s
mac / clang-build (Debug)	2m 33s
windows / msvc-build (Release)	1m 55s
ubuntu / gcc-build (ubuntu-26.04, Debug)	2m 23s
windows / msvc-build (Debug)	3m 55s
ubuntu / clang-build (ubuntu-26.04)	3m 5s
mac / clang-test	5m 59s
windows / clang-test	1m 30s
ubuntu / gcc-test (ubuntu-26.04)	2m 44s
ubuntu / clang-sanitizer-build (ubuntu-26.04)	3m 24s
ubuntu / clang-test (ubuntu-26.04)	2m 43s
windows / msvc-test	2m 9s
windows / clang-test-extended	3m 6s
ubuntu / gcc-test-extended (ubuntu-26.04)	2m 2s
ubuntu / clang-test-extended (ubuntu-26.04)	2m 30s
windows / msvc-test-extended	1m 46s
ubuntu / clang-sanitizer-test (ubuntu-26.04)	1m 39s
ubuntu / clang-sanitizer-test-extended (ubuntu-26.04)	1m 36s
ubuntu / gcc-build-codecov	4m 27s
mac / clang-test-extended	2m 12s
perf / ubuntu-gcc-build-perf-stats	1m 22s
perf / macos-clang-build-perf-stats	2m 5s
pages / build-scoreboard	28s
pages / build-doxygen-xml	31s
pages / build-sphinx	58s
pages / deploy-pages	0s
	1h 7m 23s

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