Hi,
Even though you have Private endpoint to an App service, it is still a PaaS service and it will not be able to communicate with VNET resource until and unless your App Service is linked to a VNET.
Even if you link an App service to VNET, when App service try to resolve a FQDN, it uses Azure DNS. You will need to force App service to use a custom DNS server in your VNET which can return the private IP address of the private endpoint to get this setup working.
Private Endpoint is used by the resources which are native to a VNET to access PaaS resources over private IP. In this case, both the source and destination is PaaS service, so you will need to tweak your architecture to make the source Web App native to VNET and force it to use Custom DNS for resolution where it can resolve to a Private endpoint.
Regards,
Karthik Srinivas