Yup - really a nifty way to handle exposing services.

I use MetalLB locally, and it does exactly this for its layer-2 mode: https://metallb.universe.tf/concepts/layer2/

Makes for a great little load-balancer setup on bare metal k8s. I have to lose a LOT of machines all at once for anything to go down and stay down, and my router configs use a known ipv4 address for everything, without having to care at all about which machine is actually handling it.

Proxy ARP would have the raspberry pi provide its own MAC address as the MAC for the server IP. All the traffic from the clients to the backup server would have to pass through the Pi's network interface for the duration of the session.

With this ARP stand-in, it provides the server's MAC to the client so subsequent traffic to the server doesn't need to pass through the Pi.