Feat(pt): Support fitting_net statistics. #10618

Job	Run time
Test Python (1, 3.9)	31m 36s
Test Python (1, 3.12)	42m 13s
Test Python (2, 3.9)	32m 7s
Test Python (2, 3.12)	38m 1s
Test Python (3, 3.9)	32m 42s
Test Python (3, 3.12)	46m 19s
Test Python (4, 3.9)	31m 39s
Test Python (4, 3.12)	38m 32s
Test Python (5, 3.9)	31m 35s
Test Python (5, 3.12)	36m 56s
Test Python (6, 3.9)	34m 41s
Test Python (6, 3.12)	37m 4s
Combine and update integration test durations (3.9)	5s
Combine and update integration test durations (3.12)	14s
Pass testing Python	4s
	7h 13m 48s

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