Puppeteer is node.js library to control chromium and it would work with Linux platforms. For Function app on windows, it might be hitting the sandbox limitation. We have seen similar issues with puppeteer not working with Function Windows platform. Please refer to the below article written by one of our Team members.
https://anthonychu.ca/post/azure-functions-puppeteer-pdf-razor-template/ (Please check the last section "Deploy to Azure")
So you can try deploying to Function app on Linux platform and check if it is working.