Jenkins pipeline - ssh to different machine and where to store credentials (using ssh/SSHAgent plugin/etc...)

So unfortunately, you're right.

It looks like the ssh-agent-plugin only supports stored user,passphrase,public key credentials added through the Credentials Management area in Jenkins. See this unit test that verifies that ssh-agent is working correctly based around a public key. It's unlikely that there is untested functionality in the plugin to support user+password auth.

If you can, make the switch to Public Key based authentication. If for some reason you can't switch ... you COULD install sshpass on your Jenkins box, but this is generally considered bad practice.

node {
    stage 'Does sshpass work?'
    sh 'sshpass -p \'password\' ssh user@host "ls; hostname; whois google.com;"'
}