fix: add more debug logging to TS e2e tests #1932

Job	Run time
python / Check Python chatbot	12s
python / Check Python library	51s
typescript / Check Typescript E2E tests	29s
python / Check Python E2E tests	15s
typescript / Check Typescript chatbot	30s
typescript / Check Typescript library	41s
cdk / Check Python-based Time Server	2m 3s
cdk / Check Python-based MCP Doc Server	2m 16s
cdk / Check Python-based Book Search Server	2m 2s
cdk / Check Python-based Dad Jokes Server	2m 8s
cdk / Check Typescript-based Cognito stack	18s
cdk / Check Typescript-based Cat Facts Server	1m 34s
cdk / Check Python-based Zen Server	52s
cdk / Check Typescript-based Weather Alerts Server	1m 33s
cdk / Check Typescript-based Dog Facts Server	1m 33s
cdk / Check Typescript-based Dictionary Server	1m 31s
	18m 48s

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