This is what I have in my . tmux.conf for SSH you can adapt

bind-key S command-prompt -p "ssh to:","port:" "new-window -n %1 'ssh %1 -p %2'"

That means when I press C-b, SHIFT S it asks what IP to connect to (type it in when it asks on the status bar of TMUX), press enter, the it asks the port to use.

In tmux, you usually set configuration options with set -g in tmux.conf. "-g" sets a global option which will apply to all new windows and sessions, otherwise the option applies only for the current window, which is usually not what you want.

Since command-alias is an array, you can use the -a flag to append a new value at the end.

With that said, try this:

set -ga command-alias s="new-window ssh foo"

Keep in mind that run in tmux runs a shell command in the background, so you most likely want to use something like new-window or new-session instead.