refactor: splitting up of NonlinearSolve #98

Job	Run time
test (min, ubuntu-latest, core)	19s
test (min, ubuntu-latest, adjoint)	26s
test (min, ubuntu-latest, alloc_check)	19s
test (min, macos-latest, core)	21s
test (min, macos-latest, adjoint)	24s
test (min, macos-latest, alloc_check)	23s
test (min, windows-latest, core)	48s
test (min, windows-latest, adjoint)	35s
test (min, windows-latest, alloc_check)	38s
test (1, ubuntu-latest, core)	56s
test (1, ubuntu-latest, adjoint)	50s
test (1, ubuntu-latest, alloc_check)	48s
test (1, macos-latest, core)	42s
test (1, macos-latest, adjoint)	38s
test (1, macos-latest, alloc_check)	41s
test (1, windows-latest, core)	1m 12s
test (1, windows-latest, adjoint)	1m 13s
test (1, windows-latest, alloc_check)	1m 20s
	12m 33s

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