feat(pt_expt): add fitting for energy #13918

Job	Run time
Test Python (6, 3.10)	32m 1s
Test Python (11, 3.13)	28m 23s
Test Python (2, 3.10)	34m 2s
Test Python (10, 3.10)	33m 33s
Test Python (9, 3.10)	33m 9s
Test Python (10, 3.13)	29m 55s
Test Python (5, 3.10)	34m 22s
Test Python (4, 3.10)	33m 29s
Test Python (1, 3.10)	38m 59s
Test Python (7, 3.10)	33m 59s
Test Python (12, 3.13)	29m 45s
Test Python (9, 3.13)	33m 33s
Test Python (5, 3.13)	31m 12s
Test Python (6, 3.13)	30m 18s
Test Python (8, 3.13)	30m 3s
Test Python (2, 3.13)	31m 56s
Test Python (4, 3.13)	32m 33s
Test Python (11, 3.10)	33m 0s
Test Python (3, 3.10)	32m 14s
Test Python (8, 3.10)	32m 42s
Test Python (12, 3.10)	33m 59s
Test Python (1, 3.13)	38m 10s
Test Python (7, 3.13)	31m 37s
Test Python (3, 3.13)	28m 31s
Combine and update integration test durations (3.10)	11s
Combine and update integration test durations (3.13)	6s
Pass testing Python	5s
	13h 1m 47s

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