Selfhosted
A place to share alternatives to popular online services that can be self-hosted without giving up privacy or locking you into a service you don't control.
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You're pretty much describing Tailscale with an exit node on the VPS. If the purpose of the VPS is to make their traffic not come from your home, you can omit the VPS entirely as Tailscale only routes through the VPN when reaching services also on the VPN.
Edit: to self host it, look into Headscale, but the default, hosted control server works well too.
Could you precise your answer a bit?