dsl/compiler: Fix&tidy PETSc mixed solver functionality #8056

Job	Run time
pytest-ubuntu-py310-gcc10-noomp-adjoint	34m 33s
pytest-ubuntu-py312-gcc13-omp-base	58m 27s
pytest-ubuntu-py310-gcc10-noomp-base	47m 6s
pytest-ubuntu-py311-gcc11-cxxnoomp-base	50m 45s
pytest-ubuntu-py39-gcc14-omp-base	51m 37s
pytest-ubuntu-py312-gcc12-cxxomp-adjoint	45m 53s
pytest-ubuntu-py312-gcc12-cxxomp-base	1h 3m 7s
pytest-ubuntu-py311-gcc11-cxxnoomp-adjoint	37m 28s
pytest-ubuntu-py39-gcc14-omp-adjoint	37m 33s
pytest-docker-py39-icx-omp-base	36m 13s
pytest-docker-py39-gcc-omp-base	44m 22s
pytest-ubuntu-py39-gcc9-omp-base	51m 2s
pytest-ubuntu-py39-gcc9-omp-adjoint	37m 42s
pytest-ubuntu-py312-gcc13-omp-adjoint	42m 37s
pytest-osx-py312-clang-omp-base	32m 2s
pytest-docker-py39-gcc-omp-adjoint	32m 47s
pytest-docker-py39-icx-omp-adjoint	31m 57s
	12h 15m 11s

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