test: use applicationName for MCP client identification #1934

Job	Run time
python / Check Python chatbot	11s
python / Check Python library	50s
typescript / Check Typescript E2E tests	33s
typescript / Check Typescript library	46s
typescript / Check Typescript chatbot	33s
python / Check Python E2E tests	13s
cdk / Check Python-based Dad Jokes Server	2m 10s
cdk / Check Python-based MCP Doc Server	2m 1s
cdk / Check Python-based Zen Server	55s
cdk / Check Typescript-based Cat Facts Server	1m 32s
cdk / Check Python-based Book Search Server	2m 19s
cdk / Check Typescript-based Dictionary Server	1m 33s
cdk / Check Typescript-based Cognito stack	22s
cdk / Check Python-based Time Server	2m 3s
cdk / Check Typescript-based Dog Facts Server	1m 40s
cdk / Check Typescript-based Weather Alerts Server	1m 36s
	19m 17s

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