misc: Revamp exception hierarchy #7227

Job	Run time
pytest-ubuntu-py311-gcc11-noomp-base	54m 4s
pytest-ubuntu-py311-gcc11-noomp-adjoint	40m 41s
pytest-ubuntu-py312-gcc12-omp-base	1h 10m 31s
pytest-ubuntu-py312-gcc12-omp-adjoint	51m 22s
pytest-ubuntu-py39-gcc7-omp-base	56m 19s
pytest-ubuntu-py39-gcc7-omp-adjoint	41m 13s
pytest-ubuntu-py310-gcc10-noomp-base	53m 44s
pytest-ubuntu-py310-gcc10-noomp-adjoint	39m 44s
pytest-ubuntu-py312-gcc13-omp-base	1h 11m 37s
pytest-ubuntu-py312-gcc13-omp-adjoint	51m 13s
pytest-ubuntu-py39-gcc9-omp-base	55m 7s
pytest-ubuntu-py39-gcc9-omp-adjoint	41m 0s
pytest-osx-py312-clang-omp-base	36m 48s
pytest-docker-py39-gcc-omp-base	47m 34s
pytest-docker-py39-gcc-omp-adjoint	36m 19s
pytest-docker-py39-icx-omp-base	47m 30s
pytest-docker-py39-icx-omp-adjoint	43m 38s
	13h 58m 24s

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