feat: add fields to `OverrideInit`, better `nlsolve_alg` handling #476

Job	Run time
Tests (1, Core) / Tests - Core	15m 32s
Tests (1, Downstream) / Tests - Downstream	40m 49s
Tests (1, Python) / Tests - Python	19m 5s
Tests (1, QA) / Tests - QA	12m 39s
Tests (lts, Downstream) / Tests - Downstream	22m 58s
Tests (lts, Core) / Tests - Core	7m 3s
Tests (lts, Python) / Tests - Python	7m 23s
Tests (lts, QA) / Tests - QA	6m 27s
Tests (pre, Core) / Tests - Core	15m 35s
Tests (pre, Downstream) / Tests - Downstream	40m 22s
Tests (pre, Python) / Tests - Python	19m 30s
Tests (pre, QA) / Tests - QA	12m 37s
	3h 40m 0s

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