I'm not up-to-date with the internals of tailscale, but my impression was they run additional services on top of the actual VPN (that is their "value-add" to wireguard), some of which are actual proxies, which hence blur that line in the minds of users (along with some so-called "VPN" providers who are just providing proxies).
In the modes I'm talking about, there's a real wireguard VPN that your local tailscale process is participating in. But instead of attaching it to a TAP device, there's a whole virtual networking stack inside the tailscale process.
You could treat it like running a normal VPN app inside a virtual machine. Surely that's still be a VPN, or the distinction gets weird. But if we do agree it's a VPN, a couple examples based on this one will force the distinction to get weird anyway. The line of VPN or not is surprisingly blurry.