No. You only need one prekey.

The initiating party uses an ephemeral key.

The shared secret is used to derive 2 private keys, one for initiator to target, and one for target to initiator.

When sending a message you pick the private key depending on your role in the channel, encrypt the message to the key itself, and put it in an event signed by the key. To receive messages you look for events by the other side.

This also comes with plausible deniability.

Channels can be rotated and this provides stronger security guarantees than gift wraps (sender and recipient anonymity).