How to unlock ssh passphrase only if it was not already added to ssh-agent?

Question

I have a script that collects information from multiple ssh hosts at once, so it needs the ssh passphrase to be unlocked and loaded into ssh-agent before spawning connections in parallel. All hosts have the public key installed.

Collecting remote info in parallel is achieved like this, given a list of hosts as $hostlist:

remote_infos=$(while read -r host; do ssh -nTq "$host" "$some_command" & done <<< "$hostlist"; wait) 

However, if the ssh passphrase was not unlocked, it will ask it for all hosts, not just the first one, and also the prompting for passwords will look messy.

Is there a fast way to unlock that passphrase from the script only if it is not already unlocked?

I can simply run ssh -nTq "$host" true on the first host beforehand, but it seems too much (and slow) to establish a full ssh connection just for this.

Alternatively, I can run ssh-add but that will prompt for the passphrase even if it was already added. I could maybe parse ssh-add -l to avoid that, but is there an better way?

Optional question: is there a solution for password authentication? I have seen mentions of sshpass but it does not seem very secure to do that.