refactor: splitting up of NonlinearSolve #96

Job	Run time
test (min, ubuntu-latest, core)	19s
test (min, ubuntu-latest, adjoint)	19s
test (min, ubuntu-latest, alloc_check)	22s
test (min, macos-latest, core)	21s
test (min, macos-latest, adjoint)	26s
test (min, macos-latest, alloc_check)	22s
test (min, windows-latest, core)	37s
test (min, windows-latest, adjoint)	1m 16s
test (min, windows-latest, alloc_check)	41s
test (1, ubuntu-latest, core)	52s
test (1, ubuntu-latest, adjoint)	48s
test (1, ubuntu-latest, alloc_check)	48s
test (1, macos-latest, core)	37s
test (1, macos-latest, adjoint)	40s
test (1, macos-latest, alloc_check)	37s
test (1, windows-latest, core)	1m 15s
test (1, windows-latest, adjoint)	1m 21s
test (1, windows-latest, alloc_check)	1m 22s
	13m 3s

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