dsl/compiler: Fix&tidy PETSc mixed solver functionality #8014

Job	Run time
pytest-ubuntu-py312-gcc12-cxxomp-adjoint	2m 20s
pytest-ubuntu-py310-gcc10-noomp-adjoint	2m 0s
pytest-ubuntu-py311-gcc11-cxxnoomp-adjoint	2m 0s
pytest-ubuntu-py310-gcc10-noomp-base	1m 53s
pytest-ubuntu-py39-gcc14-omp-base	2m 12s
pytest-ubuntu-py39-gcc9-omp-adjoint	2m 2s
pytest-docker-py39-gcc-omp-base	3m 32s
pytest-ubuntu-py312-gcc13-omp-adjoint	2m 10s
pytest-osx-py312-clang-omp-base	2m 23s
pytest-docker-py39-gcc-omp-adjoint	3m 27s
pytest-ubuntu-py311-gcc11-cxxnoomp-base	1m 57s
pytest-ubuntu-py39-gcc9-omp-base	1m 57s
pytest-ubuntu-py312-gcc12-cxxomp-base	2m 18s
pytest-ubuntu-py39-gcc14-omp-adjoint	2m 2s
pytest-ubuntu-py312-gcc13-omp-base	2m 3s
pytest-docker-py39-icx-omp-adjoint	3m 30s
pytest-docker-py39-icx-omp-base	3m 31s
	41m 17s

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