Despite of Ping can help you to test a ICMP protocol within Azure Vnet Itsn't the best option for TCP/HTTP protocol , So you can test doing your http call with curl (e.g. curl -v http://myweab.azurewebsites.net) if this isn't working.
You probably need to configure the path to connect privately in your vnet with one of these below mechanism:
https://learn.microsoft.com/en-us/azure/app-service/overview-vnet-integration
- Service Endpoint (https://learn.microsoft.com/en-us/azure/virtual-network/virtual-network-service-endpoints-overview)
- Private endpoint (https://learn.microsoft.com/en-us/azure/app-service/overview-private-endpoint)
Don't forget to check in your NSG attached to the vnet the rule to allow the communication to AppService tag. (https://learn.microsoft.com/en-us/azure/virtual-network/service-tags-overview)
Let me know if this help your issue.
Luis,