[Analysis] Use `verify-diagnostics` for print-based tests (NFC) #15661

Job	Run time
Runner-Preparation	1s
pre-commit (code formatting)	28s
Integration-Tests (a100-runner-set)	4m 24s
Integration-Tests (mi210)	10m 58s
Integration-Tests (h100-runner-set)	5m 57s
Build-Tests (macos-latest)	2m 52s
Integration-Tests (mi300x)	10m 23s
	35m 3s

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