Might have been better if they built on bonjour/zeroconf rather than make a "tailscale" api though... on the other hand, I guess bonjour/zeroconf works oob on tailscale anyway.
Which makes this more of a marketing for a new api/app platform?
LAN discovery is handled by Tailscale's network engine, a couple layers of abstraction below the file sending. We're going to add some mdns stuff in there at some point (similar to WebRTC's privacy-preserving LAN endpoint discovery), but the benefit of running this all over Tailscale's network engine is that file transfer works exactly the same whether you're on the same LAN as the target, or halfway across the internet. The only variable is how fast the file moves.