Someone else pointed out Tailscale; I've had luck with free tier VPS+WireGuard.
I have an Oracle one which has worked well. Downside is I did link my CC, because my account was getting deactivated due to inactivity (even using it as a VPN and nginx proxy for my self hosting wasn't enough to keep it "active"). But I stay below the free allowance, so it doesn't cost.
That said: as far as anonymity goes, it's not the right tool. And I fully appreciate the irony of trying to self-host to get away from large corporations owning my data...and relying on Oracle to do so. But you can get a static IP and VPS for free, so that's something.