I have a server that runs Proxmox and a server that runs TrueNAS, so a very similar setup to yours. As long as your LXC is tied to a network adapter that has access to your file server (it almost certainly is unless you’re using multiple NICs and/or VLANs), you should be able to mount shares inside your LXC just like you do on any other Linux machine.
Can you ping your fileserver from inside the container? If so, then the issue is with the configuration in the container itself. Privileged or unprivileged shouldn’t matter here. How are you trying to mount the CIFS share?
Edit: I see that you’re mounting the share in Proxmox and mapping it to your container. You don’t need to do this. Just mount it in the container itself.
I’m sorry, I think I gave you bad information. I have my containers set to unprivileged=no. I forgot about the “double negative” in how that flag was described.
So apparently my containers are privileged, so I don’t think I’ve ever tried to do what you are doing.