Actually that's one of the main reasons I use Syncthing: It doesn't need a server, as it is a peer-to-peer architecture. Unlike a centralised solution (cloud storage, Nextcloud, etc.) devices sync directly with each other. If they are on the same local network, you get to enjoy the full bandwidth of your local network. If they need to sync over a long distance over the internet, you are limited by the upload and download speeds of your internet provider, just like with centralised storage.

I have a server that serves as an introducer, so I don't have to connect each device with every other device manually. But the server doesn't need to be available once all devices are connected with each other.

Syncing continues to work without it for as long as I don't reinstall any of the other devices. And even if I'd reinstall a device, I could delegate any other device to be the introducer or connect the devices manually with each other. It really is quite robust and fail-safe.