refactor: splitting up of NonlinearSolve #236

Job	Run time
test (Core, 1.10, ubuntu-latest)	11m 46s
test (Core, 1.10, macos-latest)	10m 9s
test (Core, 1.10, windows-latest)	16m 35s
test (Core, 1, ubuntu-latest)	16m 21s
test (Core, 1, macos-latest)	12m 3s
test (Core, 1, windows-latest)	19m 46s
test (Downstream, 1.10, ubuntu-latest)	7m 51s
test (Downstream, 1.10, macos-latest)	5m 3s
test (Downstream, 1.10, windows-latest)	10m 28s
test (Downstream, 1, ubuntu-latest)	16m 16s
test (Downstream, 1, macos-latest)	10m 1s
test (Downstream, 1, windows-latest)	19m 16s
test (Wrappers, 1.10, ubuntu-latest)	9m 15s
test (Wrappers, 1.10, macos-latest)	6m 3s
test (Wrappers, 1.10, windows-latest)	11m 43s
test (Wrappers, 1, ubuntu-latest)	16m 34s
test (Wrappers, 1, macos-latest)	8m 14s
test (Wrappers, 1, windows-latest)	19m 26s
	3h 46m 50s

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