feat: implement SII for `SCCNonlinearProblem` #509

Job	Run time
Tests (1, Core) / Tests - Core	8m 41s
Tests (1, Downstream) / Tests - Downstream	32m 57s
Tests (1, Python) / Tests - Python	11m 38s
Tests (1, QA) / Tests - QA	5m 55s
Tests (lts, Core) / Tests - Core	8m 54s
Tests (lts, Downstream) / Tests - Downstream	27m 58s
Tests (lts, Python) / Tests - Python	9m 0s
Tests (pre, Core) / Tests - Core	8m 42s
Tests (pre, Downstream) / Tests - Downstream	33m 56s
Tests (lts, QA) / Tests - QA	6m 17s
Tests (pre, QA) / Tests - QA	7m 43s
Tests (pre, Python) / Tests - Python	11m 39s
	2h 53m 20s

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