refactor: splitting up of NonlinearSolve #239

Job	Run time
downgrade (1.10, Core)	15s
test (Core, 1.10, ubuntu-latest)	3m 0s
downgrade (1.10, Downstream)	24s
test (Core, 1.10, macos-latest)	1s
downgrade (1.10, Wrappers)	16s
test (Core, 1.10, windows-latest)	2m 50s
test (Core, 1, ubuntu-latest)	2m 49s
test (Core, 1, macos-latest)	1s
test (Core, 1, windows-latest)	2m 36s
test (Downstream, 1.10, ubuntu-latest)	2m 44s
test (Downstream, 1.10, macos-latest)	1s
test (Downstream, 1.10, windows-latest)	2m 29s
test (Downstream, 1, ubuntu-latest)	2m 26s
test (Downstream, 1, macos-latest)	1s
test (Downstream, 1, windows-latest)	58s
test (Wrappers, 1.10, ubuntu-latest)	54s
test (Wrappers, 1.10, macos-latest)	1s
test (Wrappers, 1.10, windows-latest)	46s
test (Wrappers, 1, ubuntu-latest)	45s
test (Wrappers, 1, macos-latest)	1s
test (Wrappers, 1, windows-latest)	33s
	23m 51s

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