"Routing everything through your laptop" is not how Tailscale works. I'm not sure where your understanding has gone wrong so I can't really be more helpful.
There is this „without tailscale“ and „with tailscale“ comparison.
Ah, I see what you're looking at. That diagram can be confusing because it only shows the tunnels from your laptop to other devices; it doesn't show that every device has a tunnel to every other device.