misc: Revamp exception hierarchy #7210

Job	Run time
pytest-ubuntu-py311-gcc11-noomp-base	4m 1s
pytest-ubuntu-py311-gcc11-noomp-adjoint	4m 0s
pytest-ubuntu-py312-gcc12-omp-base	4m 2s
pytest-ubuntu-py312-gcc12-omp-adjoint	4m 1s
pytest-ubuntu-py39-gcc7-omp-base	4m 1s
pytest-ubuntu-py39-gcc7-omp-adjoint	4m 2s
pytest-ubuntu-py310-gcc10-noomp-base	4m 2s
pytest-ubuntu-py310-gcc10-noomp-adjoint	4m 2s
pytest-ubuntu-py312-gcc13-omp-base	4m 1s
pytest-ubuntu-py312-gcc13-omp-adjoint	4m 0s
pytest-ubuntu-py39-gcc9-omp-base	4m 2s
pytest-ubuntu-py39-gcc9-omp-adjoint	4m 2s
pytest-osx-py312-clang-omp-base	4m 3s
pytest-docker-py39-gcc-omp-base	4m 2s
pytest-docker-py39-gcc-omp-adjoint	4m 2s
pytest-docker-py39-icx-omp-base	4m 4s
pytest-docker-py39-icx-omp-adjoint	4m 4s
	1h 8m 31s

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