Thank you @oheil !
SFTP (and fileZila) password authentification works very well. Indeed key exchange is tried first and fail, this is why password authentification is finally selected. It seems that Julia download() function is much more picky…
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug1: Authentications that can continue: publickey,password
debug1: Next authentication method: publickey
debug1: Offering public key: /home/user/.ssh/id_rsa RSA SHA256:XE...
debug1: Authentications that can continue: publickey,password
debug1: Trying private key: /home/user/.ssh/id_dsa
debug1: Trying private key: /home/user/.ssh/id_ecdsa
debug1: Trying private key: /home/user/.ssh/id_ecdsa_sk
debug1: Trying private key: /home/user/.ssh/id_ed25519
debug1: Trying private key: /home/user/.ssh/id_ed25519_sk
debug1: Trying private key: /home/user/.ssh/id_xmss
debug1: Next authentication method: password
user@xx.xx.xx.xx's password:
debug1: Enabling compression at level 6.
Authenticated to xx.xx.xx.xx ([xx.xx.xx.xx]:22) using "password".