refactor(optimizer): finalize optimizer schema and backend handling #13704

Job	Run time
Test Python (3, 3.13)	29m 20s
Test Python (2, 3.13)	19m 17s
Test Python (1, 3.10)	20m 26s
Test Python (3, 3.10)	15m 20s
Test Python (6, 3.13)	16m 49s
Test Python (7, 3.13)	18m 29s
Test Python (1, 3.13)	17m 52s
Test Python (8, 3.10)	24m 6s
Test Python (10, 3.13)	21m 34s
Test Python (7, 3.10)	15m 50s
Test Python (12, 3.13)	19m 31s
Test Python (9, 3.10)	20m 3s
Test Python (6, 3.10)	19m 35s
Test Python (4, 3.10)	17m 39s
Test Python (11, 3.13)	19m 28s
Test Python (11, 3.10)	18m 1s
Test Python (2, 3.10)	14m 50s
Test Python (12, 3.10)	16m 57s
Test Python (10, 3.10)	18m 49s
Test Python (5, 3.10)	15m 21s
Test Python (4, 3.13)	18m 12s
Test Python (9, 3.13)	17m 22s
Test Python (5, 3.13)	18m 12s
Test Python (8, 3.13)	15m 1s
Combine and update integration test durations	1s
Pass testing Python	5s
	7h 28m 10s

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