Have a separate small travel router with embedded VPN support to connect printer to Wi-fi hotspot with whatever region it wants to see.
It's not HP's or any other vendor's business to know where you are. This is an easy solution to this.
I have a few routers at home with a separate Wifi hotspot each configured for separate country to avoid exactly this nonsense for different services.
Advantage of this approach is you can travel with a small travel router all over the world while feeding each of the service with a consistent country location.
Doesn't sound like it has to be online if they're blocking it using a VPN. But probably it phones home opportunistically, similar to modern TVs and most other "smart" stuff.
I have about 5 of these at home, each configured at different subnet and VPN for different country. One i always take with me while traveling to securely connect via shady hotel Wi-Fi's.
You can even go crazy with it - install ZeroTier directly in the router by typing few commands and access low-level config of the router from anywhere.
AMZN carefully watches the marketplace for "wonders" who are monetizing inefficiencies and if these inefficiencies worth big enough profit, AMZN will fill the gap themselves.
Platform is never your friend or "partner" even if they say so.
Would installing WireGuard server on a router directly solve this (like Gl-Inet travel routers)?