gnupg – Generate GPG key without saving to keychain

I am trying to generate a GPG key with gnupg. However, instead of exporting the secret key to a file, I am trying to pipe it to another program (keybase pgp import) that will process it.

Right now, I am using gpg --full-gen-key --expert -o -.

However, the piped output is not what I was looking for:

pub   ed25519 2021-08-27 (SC)
      0123456789ABCDEF0123456789ABCDEF01234567
uid                      Allice Bobeve
sub   cv25519 2021-08-27 (E)

The secret key is exported to my keychain instead of to stdout as I intended.

What is the correct gnupg command to generate a secret key and export it directly into stdout, without storing it in my local keychain?
In your answer, please explain all flags and options. I would still like to use the interactive prompts for selecting a key type and size (or curve type), creating a UID, etc.

Migrated from https://stackoverflow.com/questions/68958557