> So, somewhere on that website, there’s a free version that can be downloaded onto a desktop and run without signing up for their service?

If you go to https://tailscale.com/pricing?plan=personal

The first plan on the left called 'Personal' is free.

It uses a central orchestrator which is what requires you to sign up. If you prefer to self host your orchestrator you can look into Headscale, an alternative that seeks to be compatible with the clients.

> So, basically you leave a computer running at home, and this thing lets you pretend to be running your internet stuff through it while you’re on the road?

That's one thing you can do with it, yes. You can also run custom DNS entries across it, ACLs, it is very flexible.

The service is free up to certain amount of connected people and devices. You most likely don't need to pay for it. I am pretty heavy user and don't. It is virtual private network orchestrator. It allows you to connect to other devices that you add to your network as long as they are connected to the internet. So your office computer, home server or NAS. If you have some home automation like home assistant you can connect to it from anywhere. That kind of stuff.

You can run it on a capable router or on a RPi, or on your NAS. It's especially useful if you want to self-host (e.g. Immich). You can use it to authenticate for ssh if you like, or simply give you an IP you can ssh to.

It's especially handy if you want a secondary way in, in case you have problems connecting using wireguard, since it supports using a relay if you're stuck in a hotel with a heavily restricted connection.

If you run DNS at home, you can even configure it to use your home DNS and route to your home subnet(s).