@Dávid Tamás László Thank you for reaching out to Microsoft Q&A, apologize for any inconvenience caused on this.
To reproduce this behavior, I have followed the same documentation steps and deployed the nodejs app from visual studio code to app service and it got deployed successfully without any issues.
I have gone through recorded video and found that in our documentation, we are using express generator to create an app which is installed with Node.js and NPM and i don't see you are using it.
Based on the shared information in the recorded video, I have looked at the backend logs and get to know that webapp was down due to the error message "iisnode was unable to establish named pipe connection to the node.exe process before the process terminated"
iisnode - IISNODE is a native IIS module that allows hosting of node.js applications on App Service Windows in IIS. Typically, the error indicates (from this module, that something wrong in the node configuration or an application error.
I would suggest you add the web.config file in your application by referring to this sample schema about web.config file
Refer to this sample blog post for deploying nodejs applications using NestJS framework or using React JS framework.
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Feel free to reach back to me if you have any further questions on this.