refactor: splitting up of NonlinearSolve #248

Job	Run time
downgrade (1.10, core)	16m 0s
downgrade (1.10, downstream)	8m 35s
test (core, 1.10, ubuntu-latest)	15m 24s
downgrade (1.10, wrappers)	23m 28s
test (core, 1.10, macos-latest)	12m 20s
test (core, 1.10, windows-latest)	21m 21s
test (core, 1, ubuntu-latest)	28m 40s
test (core, 1, macos-latest)	20m 37s
test (core, 1, windows-latest)	32m 10s
test (downstream, 1.10, ubuntu-latest)	7m 51s
test (downstream, 1.10, macos-latest)	5m 20s
test (downstream, 1.10, windows-latest)	11m 8s
test (downstream, 1, ubuntu-latest)	17m 46s
test (downstream, 1, macos-latest)	9m 38s
test (downstream, 1, windows-latest)	23m 15s
test (wrappers, 1.10, ubuntu-latest)	9m 20s
test (wrappers, 1.10, macos-latest)	8m 41s
test (wrappers, 1.10, windows-latest)	12m 10s
test (wrappers, 1, ubuntu-latest)	20m 16s
test (wrappers, 1, macos-latest)	13m 4s
test (wrappers, 1, windows-latest)	22m 22s
	5h 39m 26s

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