dsl/compiler: Fix&tidy PETSc mixed solver functionality #8055

Job	Run time
pytest-ubuntu-py312-gcc12-cxxomp-adjoint	14m 58s
pytest-ubuntu-py311-gcc11-cxxnoomp-base	14m 58s
pytest-ubuntu-py312-gcc13-omp-base	14m 58s
pytest-ubuntu-py310-gcc10-noomp-adjoint	14m 59s
pytest-ubuntu-py312-gcc12-cxxomp-base	14m 58s
pytest-ubuntu-py310-gcc10-noomp-base	14m 59s
pytest-docker-py39-icx-omp-base	15m 0s
pytest-ubuntu-py312-gcc13-omp-adjoint	15m 0s
pytest-osx-py312-clang-omp-base	15m 1s
pytest-docker-py39-gcc-omp-adjoint	15m 1s
pytest-ubuntu-py311-gcc11-cxxnoomp-adjoint	14m 58s
pytest-docker-py39-icx-omp-adjoint	15m 0s
pytest-ubuntu-py39-gcc9-omp-adjoint	15m 0s
pytest-docker-py39-gcc-omp-base	15m 0s
pytest-ubuntu-py39-gcc14-omp-base	14m 58s
pytest-ubuntu-py39-gcc14-omp-adjoint	14m 58s
pytest-ubuntu-py39-gcc9-omp-base	14m 59s
	4h 14m 45s

Provide feedback