refactor: splitting up of NonlinearSolve #84

Job	Run time
test (min, ubuntu-latest, core)	26s
test (min, ubuntu-latest, adjoint)	21s
test (min, ubuntu-latest, alloc_check)	24s
test (min, macos-latest, core)	21s
test (min, macos-latest, adjoint)	22s
test (min, macos-latest, alloc_check)	19s
test (min, windows-latest, core)	35s
test (min, windows-latest, adjoint)	45s
test (min, windows-latest, alloc_check)	41s
test (1, ubuntu-latest, core)	50s
test (1, ubuntu-latest, adjoint)	55s
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)	38s
test (1, windows-latest, core)	1m 30s
test (1, windows-latest, adjoint)	1m 26s
test (1, windows-latest, alloc_check)	1m 24s
	13m 4s

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