refactor: splitting up of NonlinearSolve #246

Job	Run time
downgrade (1.10, core)	16m 49s
downgrade (1.10, downstream)	8m 23s
downgrade (1.10, wrappers)	9m 51s
test (core, 1.10, ubuntu-latest)	15m 36s
test (core, 1.10, macos-latest)	9m 48s
test (core, 1.10, windows-latest)	19m 10s
test (core, 1, ubuntu-latest)	20m 42s
test (core, 1, macos-latest)	4m 30s
test (core, 1, windows-latest)	26m 50s
test (downstream, 1.10, ubuntu-latest)	7m 53s
test (downstream, 1.10, macos-latest)	1s
test (downstream, 1.10, windows-latest)	11m 34s
test (downstream, 1, ubuntu-latest)	17m 28s
test (downstream, 1, macos-latest)	1s
test (downstream, 1, windows-latest)	22m 29s
test (wrappers, 1.10, ubuntu-latest)	9m 25s
test (wrappers, 1.10, macos-latest)	1s
test (wrappers, 1.10, windows-latest)	12m 52s
test (wrappers, 1, ubuntu-latest)	19m 23s
test (wrappers, 1, macos-latest)	1s
test (wrappers, 1, windows-latest)	22m 13s
	4h 15m 0s

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