api: Add (rudimentary) autopickling support #8889

Job	Run time
pytest-ubuntu-py311-gcc10-noomp-base	39m 53s
pytest-ubuntu-py311-gcc11-cxxnoomp-base	42m 51s
pytest-ubuntu-py311-gcc10-noomp-adjoint	27m 52s
pytest-ubuntu-py310-gcc9-omp-adjoint	29m 48s
pytest-ubuntu-py312-gcc13-omp-base	48m 25s
pytest-ubuntu-py312-gcc12-cxxomp-base	52m 45s
pytest-ubuntu-py311-gcc11-cxxnoomp-adjoint	30m 47s
pytest-ubuntu-py312-gcc13-omp-adjoint	33m 22s
pytest-ubuntu-py310-gcc9-omp-base	42m 21s
pytest-docker-py310-icx-omp-base	29m 40s
pytest-ubuntu-py310-gcc14-omp-base	40m 51s
pytest-ubuntu-py313-gcc14-omp-base	50m 12s
pytest-osx-py312-clang-omp-base	34m 16s
pytest-ubuntu-py310-gcc14-omp-adjoint	29m 49s
pytest-docker-py310-gcc-omp-base	31m 58s
pytest-docker-py310-icx-omp-adjoint	26m 22s
pytest-ubuntu-py312-gcc12-cxxomp-adjoint	37m 20s
pytest-ubuntu-py313-gcc14-omp-adjoint	34m 56s
pytest-docker-py310-gcc-omp-adjoint	25m 3s
	11h 28m 31s

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