misc: Add MPI0 logging level #5796

Job	Run time
pytest-ubuntu-py311-gcc11-noomp-base	43m 15s
pytest-ubuntu-py311-gcc11-noomp-adjoint	43m 14s
pytest-ubuntu-py38-gcc12-omp-base	43m 14s
pytest-ubuntu-py38-gcc12-omp-adjoint	43m 14s
pytest-ubuntu-py37-gcc7-omp-base	43m 12s
pytest-ubuntu-py37-gcc7-omp-adjoint	43m 15s
pytest-ubuntu-py310-gcc10-noomp-base	43m 14s
pytest-ubuntu-py310-gcc10-noomp-adjoint	43m 16s
pytest-ubuntu-py38-gcc8-omp-base	43m 14s
pytest-ubuntu-py38-gcc8-omp-adjoint	43m 13s
pytest-ubuntu-py39-gcc9-omp-base	43m 14s
pytest-ubuntu-py39-gcc9-omp-adjoint	43m 12s
pytest-osx-py37-clang-omp-base	5m 7s
pytest-docker-py39-gcc-omp-base	43m 15s
pytest-docker-py39-gcc-omp-adjoint	43m 15s
pytest-docker-py39-icx-omp-base	43m 14s
pytest-docker-py39-icx-omp-adjoint	43m 20s
	11h 36m 58s

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