refactor: splitting up of NonlinearSolve #93

Job	Run time
test (min, ubuntu-latest, core)	26s
test (min, ubuntu-latest, adjoint)	23s
test (min, ubuntu-latest, alloc_check)	20s
test (min, macos-latest, core)	32s
test (min, macos-latest, adjoint)	22s
test (min, macos-latest, alloc_check)	20s
test (min, windows-latest, core)	47s
test (min, windows-latest, adjoint)	41s
test (min, windows-latest, alloc_check)	41s
test (1, ubuntu-latest, core)	48s
test (1, ubuntu-latest, adjoint)	49s
test (1, ubuntu-latest, alloc_check)	52s
test (1, macos-latest, core)	39s
test (1, macos-latest, adjoint)	54s
test (1, macos-latest, alloc_check)	45s
test (1, windows-latest, core)	1m 34s
test (1, windows-latest, adjoint)	1m 16s
test (1, windows-latest, alloc_check)	1m 18s
	13m 27s

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