[SteveBronder]

Summary

Grouped unit executables expose duplicate helper definitions, conflicting MPI registrations, and autodiff state left behind by earlier tests. Inline shared helpers, give MPI fixtures and call IDs distinct names, and use the autodiff cleanup fixture for the affected OpenCL tests. Guarantee that the Bernoulli GLM invalid-label fixture contains an invalid label.

Part 5 of the CMake migration split from #3463.

Targets cmake-split/04-probability-tests (#3504) as the preceding layer of the native stack. The review contains only this layer's prepared patch and its supporting tests.

Tests

• Reproduced shared-helper duplicate definitions; fixed helpers link and execute across translation units.
• Independent Make Bernoulli GLM suite passes all 24 tests.
• The combined stack passes seven grouped MPI tests with two local ranks.
• OpenCL autodiff cleanup runtime coverage remains for GPU CI.

Side Effects

Test fixtures, registration IDs, and cleanup behavior change. Production Math code is unaffected.

Release notes

Make unit tests safe to link and execute in shared test processes.

Checklist

• Copyright holder: Simons Foundation
• The complete basic-test and CI matrix is passing
• C++ idioms and Doxygen documentation have completed review
• Focused validation is passing as described above; remaining coverage is listed

Related PRs

• 1/7: [CMake 1/7] Fix test compilation with strict compiler warnings
• 2/7: [CMake 2/7] Share OpenCL kernel-cache registration across translation units
• 3/7: [CMake 3/7] Isolate TBB construction tests from process-wide initialization
• 4/7: [CMake 4/7] Make probability test fixtures safe for grouped linking
• 5/7: [CMake 5/7] Make unit tests safe for grouped execution (this PR)
• 6/7: [CMake 6/7] Initialize CVODES adjoint quadrature derivative buffers
• 7/7: [CMake 7/7] Add CMake builds and migrate the test runner and CI

Native stack: https://github.com/stan-dev/math/stack/3509