Thanks for sharing these details! Express.js apps need to be modified slightly to adapt to a serverless environment. I recommend following the Using Express.js with Vercel guide for the structure of your server project. Switching from an /app directory to an /api directory will indicate the index.ts file is the a serverless function instead of a static file.
You can see what Serverless Functions were detected for a deployment from the dashboard. Go to the overview page for the deployment, then expand the Deployment Summary, and expand Functions to see the paths for all functions that were created. If none are shown, then there were none detected when the site was building.
You can also check the structure of the deployed site by navigating over to the Source tab, then toggling over to the Output file tree. Symbols next to the file names indicate whether something is a static file, a serverless function, or middleware.