chore(deps): bump typescript in /examples/servers/auth #1385

Job	Run time
typescript / Check Typescript chatbot	36s
python / Check Python chatbot	15s
python / Check Python library	48s
typescript / Check Typescript E2E tests	40s
cdk / Check Typescript-based Cognito stack	47s
typescript / Check Typescript library	48s
python / Check Python E2E tests	15s
cdk / Check Python-based Time Server	1m 57s
cdk / Check Python-based Book Search Server	2m 33s
cdk / Check Python-based MCP Doc Server	2m 4s
cdk / Check Typescript-based Cat Facts Server	1m 43s
cdk / Check Typescript-based Weather Alerts Server	1m 35s
cdk / Check Python-based Dad Jokes Server	2m 7s
cdk / Check Typescript-based Dog Facts Server	1m 33s
cdk / Check Python-based Zen Server	35s
cdk / Check Typescript-based Dictionary Server	1m 52s
	20m 8s

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