Run ssh and immediately execute command

ssh -t 'command; bash -l'

will execute the command and then start up a login shell when it completes. For example:

ssh -t [email protected] 'cd /some/path; bash -l'

This isn't quite what you're looking for, but I've found it useful in similar circumstances.

I recently added the following to my $HOME/.bashrc (something similar should be possible with shells other than bash):

if [ -f $HOME/.add-screen-to-history ] ; then
    history -s 'screen -dr'
fi

I keep a screen session running on one particular machine, and I've had problems with ssh connections to that machine being dropped, requiring me to re-run screen -dr every time I reconnect.

With that addition, and after creating that (empty) file in my home directory, I automatically have the screen -dr command in my history when my shell starts. After reconnecting, I can just type Control-P Enter and I'm back in my screen session -- or I can ignore it. It's flexible, but not quite automatic, and in your case it's easier than typing tmux list-sessions.

You might want to make the history -s command unconditional.

This does require updating your $HOME/.bashrc on each of the target systems, which might or might not make it unsuitable for your purposes.