Send a file straight from this browser to another one over a direct WebRTC connection. The file is encrypted with AES-256-GCM before it leaves, and the key travels separately from the connection code, so neither one alone is enough to read anything.
Direct, and encrypted regardless. The connection is peer to peer, and the file is encrypted with AES-256-GCM before it is sent, so the bytes crossing the network are ciphertext no matter what the transport does. Signalling is done by you pasting two short codes, so no server holds a record of who connected to whom.
A public STUN server helps the two browsers find each other. It learns that two addresses wish to connect. It never sees the file, the key, or the contents. On the same local network the connection often forms without it.
Some networks will simply refuse. Behind symmetric NAT or locked-down corporate Wi-Fi a direct path may be impossible. There is no relay fallback, so the connection fails openly rather than quietly routing your file through somebody else's server. Both tabs must also stay open, nothing is stored for later pickup.