compiler: Rework multi-level buffering #5883

Job	Run time
pytest-ubuntu-py311-gcc11-noomp-base	55m 23s
pytest-ubuntu-py311-gcc11-noomp-adjoint	1h 2m 5s
pytest-ubuntu-py38-gcc12-omp-base	1h 9m 10s
pytest-ubuntu-py38-gcc12-omp-adjoint	52m 35s
pytest-ubuntu-py37-gcc7-omp-base	59m 24s
pytest-ubuntu-py37-gcc7-omp-adjoint	56m 10s
pytest-ubuntu-py310-gcc10-noomp-base	55m 45s
pytest-ubuntu-py310-gcc10-noomp-adjoint	51m 36s
pytest-ubuntu-py38-gcc8-omp-base	51m 43s
pytest-ubuntu-py38-gcc8-omp-adjoint	51m 38s
pytest-ubuntu-py39-gcc9-omp-base	1h 5m 42s
pytest-ubuntu-py39-gcc9-omp-adjoint	46m 46s
pytest-osx-py37-clang-omp-base	5m 36s
pytest-docker-py39-gcc-omp-base	1h 6m 12s
pytest-docker-py39-gcc-omp-adjoint	48m 50s
pytest-docker-py39-icx-omp-base	1h 6m 49s
pytest-docker-py39-icx-omp-adjoint	50m 1s
	15h 15m 25s

Provide feedback