refactor: splitting up of NonlinearSolve #226

Job	Run time
test (Core, lts, ubuntu-latest)	20s
test (Core, lts, macos-latest)	18s
test (Core, lts, windows-latest)	1m 0s
test (Core, 1, ubuntu-latest)	50s
test (Core, 1, macos-latest)	38s
test (Core, 1, windows-latest)	1m 12s
test (Downstream, lts, ubuntu-latest)	25s
test (Downstream, lts, macos-latest)	19s
test (Downstream, lts, windows-latest)	43s
test (Downstream, 1, ubuntu-latest)	55s
test (Downstream, 1, macos-latest)	36s
test (Downstream, 1, windows-latest)	1m 20s
test (Misc, lts, ubuntu-latest)	20s
test (Misc, lts, macos-latest)	19s
test (Misc, lts, windows-latest)	34s
test (Misc, 1, ubuntu-latest)	58s
test (Misc, 1, macos-latest)	41s
test (Misc, 1, windows-latest)	1m 24s
test (Wrappers, lts, ubuntu-latest)	18s
test (Wrappers, lts, macos-latest)	20s
test (Wrappers, lts, windows-latest)	38s
test (Wrappers, 1, ubuntu-latest)	54s
test (Wrappers, 1, macos-latest)	36s
test (Wrappers, 1, windows-latest)	1m 18s
	16m 56s

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