Even if your kindle is on older firmware that doesn’t have some of the kernel extensions needed by Tailscale to create the .. TUN ? Type network interface, you can still kind of get it working in the user space mode with .. -tun -userspace-networking

And then I see my koreader calibre is pointing at localhost:8081.. so maybe there was a proxy?

It’s been a while since I set it up. But it’s possible