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.