One could possibly apply the VPN label because you go through layers of connections on a private network to go back onto the internet. I did a cursory search of the TOR website and can't find anything labeling it a VPN. But that is one of the big projects that kinda started all of this.
In fact, TOR describes an overlay network, and that's how projects like Nebula also describe their functionality. Granted, Nebula is more like a VPN than "VPN providers" also.
"VPN providers" provide a service for accessing the public internet as proxies, tunnels, etc, for evading region blocks, getting around privacy destroying things, and all that stuff. I won't knock their value. I've use them when needing internet over an open WIFI access point. I'm generally not involved in activist activities nor otherwise in harms way, so I don't have much else use of them.
But I do have use of a virtual private network. As in the core idea of it. I have a private network at home. It's not publicly available. I use Tailscale, currently, to access it when not connected directly to my home network (as in, not at home). My portable device becomes a member of a private network that has access to my private home network. This is a VPN.
I really think VPN was (incorrectly) chosen for secured proxy services because it's a simple and familiar name. The marketing using the terms "virtual private network" came far later to describe a way to secure your privacy. But it's diluted the actual technical term.