No no you understand me wrongly.
It was not by installing Electrum (NOT seed phrase). It was by verifiyng the signature with GPG just after the "Generate new key pair".
They ask me to create a secret phrase (I had to choose it myself). It was not by using Electrum but well GPG.
I think it's a new step.
GPG keys can be created but with skipping the password step, by using the command line
gpg --gen-key and following the on-screen instructions listed.
I believe that verifying the key does not require your own key (and hence password) either - at least on command-line (I once verified a message from someone else's public key without my own key, but maybe I'm misremembering. I do know that you have to set the key to be trusted while importing it though.