After my validation, when the app service on Linux is integrated with a virtual network. There is an extra NIC binding to the app service. It's IP address from APIPA address range. It looks like a design behavior as the app service on Linux is running in a standard Docker Container, read here. Also, for a normal app service is a multi-tenant environment, you can not get a dedicated IP address unless you are using a dedicated environment---ASE, read here.
![enter image description here](https://i.stack.imgur.com/AlHPO.jpg)
Furthermore, from how regional VNet Integration works, you will see the app service integrated with a vNet is not the same as a VM from a VNet.
Regional VNet Integration works by mounting virtual interfaces with
addresses in the delegated subnet. Because the from address is in your
VNet, it can access most things in or through your VNet like a VM in
your VNet would. The networking implementation is different than
running a VM in your VNet. That's why some networking features aren't
yet available for this feature.
In this case, if you wan assign a private IP address for app service, you can use Azure Private Endpoint with web apps(Preview). Read this blog for more details.
Azure Private Endpoint provides private IP address access by using a
network interface controller (NIC) attached to a virtual network
subnet for an Azure web app, allowing access from an on-premise VPN or
ExpressRoute. Implementing an endpoint effectively blocks the public
inbound access. This technology is very similar to an internal App
Service Environment (ASE) but much cheaper.