Each time you send a packet over the internet, several routers handle this packet without touching the source and destination IP addresses.
There is nothing stopping him from configuring the VPS in a way that forwards packets from the home server, rewriting the destination IP (and optionally destination port as well) but leaving the source IP intact.
For outgoing packets, the VPS should rewrite the source (homeserver) IP and port and leave the destination intact.
With iptables, this is done with MASQUERADE rules.
This is pretty much how any NAT, including ones behind home routers, work.
You then configure the homeserver to use the VPS as a gateway over wireguard, which should achieve the desired result.