refactor: splitting up of NonlinearSolve #97

Job	Run time
test (min, ubuntu-latest, core)	21s
test (min, ubuntu-latest, adjoint)	32s
test (min, ubuntu-latest, alloc_check)	19s
test (min, macos-latest, core)	20s
test (min, macos-latest, adjoint)	28s
test (min, macos-latest, alloc_check)	24s
test (min, windows-latest, core)	39s
test (min, windows-latest, adjoint)	40s
test (min, windows-latest, alloc_check)	41s
test (1, ubuntu-latest, core)	58s
test (1, ubuntu-latest, adjoint)	50s
test (1, ubuntu-latest, alloc_check)	50s
test (1, macos-latest, core)	38s
test (1, macos-latest, adjoint)	39s
test (1, macos-latest, alloc_check)	39s
test (1, windows-latest, core)	1m 26s
test (1, windows-latest, adjoint)	1m 22s
test (1, windows-latest, alloc_check)	1m 26s
	13m 12s

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