You're correct.
Most people only search for "VPN" because thats the term that got marketed for decades.
But the problem can be solved by using a proxy as well.
The intent of my comment was just to point to a second term - "proxy" - that can be used to find more valid, alternative solutions to the problem of making your homelab hosted services publicly available. And I think you agree with me, that proxy is the term closer to the usecase, even though we both correctly state that a VPN can be used as a proxy.
To make a bad analogy (it's the first thing that came to mind): It's like people buying a wok, even though they really just need a pan. And so they only search for wok, because every company says wok all the time, even though they will never use the wok as a wok, but just as a normal pan.
Even by your definition that should be a VPN, right?
... in my case, I have a homelab, a VPS and a user of a service that runs on my homelab. The VPS is just a proxy for the homelab. The user (client) talks to the homelab (server), through the VPS (proxy) so not, not really a VPN, even if I'd set up openVPN between VPS and homelab. They are not two clients.