misc: Revamp exception hierarchy #7239

Job	Run time
pytest-ubuntu-py311-gcc11-noomp-base	53m 23s
pytest-ubuntu-py311-gcc11-noomp-adjoint	40m 38s
pytest-ubuntu-py312-gcc12-omp-base	1h 9m 48s
pytest-ubuntu-py312-gcc12-omp-adjoint	51m 42s
pytest-ubuntu-py39-gcc7-omp-base	55m 44s
pytest-ubuntu-py39-gcc7-omp-adjoint	40m 10s
pytest-ubuntu-py310-gcc10-noomp-base	54m 14s
pytest-ubuntu-py310-gcc10-noomp-adjoint	39m 35s
pytest-ubuntu-py312-gcc13-omp-base	1h 9m 46s
pytest-ubuntu-py312-gcc13-omp-adjoint	50m 30s
pytest-ubuntu-py39-gcc9-omp-base	55m 10s
pytest-ubuntu-py39-gcc9-omp-adjoint	41m 13s
pytest-osx-py312-clang-omp-base	34m 35s
pytest-docker-py39-gcc-omp-base	47m 56s
pytest-docker-py39-gcc-omp-adjoint	36m 25s
pytest-docker-py39-icx-omp-base	47m 36s
pytest-docker-py39-icx-omp-adjoint	42m 25s
	13h 50m 50s

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