refactor: splitting up of NonlinearSolve #213

Job	Run time
test (Core, min, ubuntu-latest)	25s
test (Core, min, macos-latest)	19s
test (Core, min, windows-latest)	34s
test (Core, 1, ubuntu-latest)	48s
test (Core, 1, macos-latest)	38s
test (Core, 1, windows-latest)	1m 9s
test (Downstream, min, ubuntu-latest)	19s
test (Downstream, min, macos-latest)	20s
test (Downstream, min, windows-latest)	34s
test (Downstream, 1, ubuntu-latest)	56s
test (Downstream, 1, macos-latest)	36s
test (Downstream, 1, windows-latest)	1m 17s
test (Misc, min, ubuntu-latest)	19s
test (Misc, min, macos-latest)	19s
test (Misc, min, windows-latest)	37s
test (Misc, 1, ubuntu-latest)	47s
test (Misc, 1, macos-latest)	42s
test (Misc, 1, windows-latest)	1m 29s
test (Wrappers, min, ubuntu-latest)	19s
test (Wrappers, min, macos-latest)	18s
test (Wrappers, min, windows-latest)	35s
test (Wrappers, 1, ubuntu-latest)	56s
test (Wrappers, 1, macos-latest)	38s
test (Wrappers, 1, windows-latest)	1m 21s
	16m 15s

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