test: add detailed debugging for e2e TypeScript tests #1933

Job	Run time
typescript / Check Typescript E2E tests	31s
typescript / Check Typescript chatbot	34s
typescript / Check Typescript library	42s
python / Check Python E2E tests	15s
cdk / Check Typescript-based Dog Facts Server	1m 29s
python / Check Python chatbot	10s
cdk / Check Python-based MCP Doc Server	2m 1s
python / Check Python library	58s
cdk / Check Typescript-based Weather Alerts Server	1m 39s
cdk / Check Python-based Book Search Server	2m 0s
cdk / Check Python-based Time Server	2m 17s
cdk / Check Typescript-based Dictionary Server	1m 36s
cdk / Check Typescript-based Cat Facts Server	1m 33s
cdk / Check Python-based Dad Jokes Server	2m 2s
cdk / Check Python-based Zen Server	54s
cdk / Check Typescript-based Cognito stack	21s
	19m 2s

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