You don’t have to be interested in mooting to be interested in litigation. In fact, unless you want to get your advocacy rights, the presenting your arguments part of mooting has very little practical similarities to what litigation lawyers do.
You might have studied modules that are more closely aligned to litigation and enjoyed them. You could have read cases that just interest you. You could enjoy the processes and responsbilities of what a litigation lawyer does more so than what a transactional lawyer does. Try to explain why the topic/processes interest you.
Also, you don’t have to be interested in litigation to apply to HSF - they have plenty of other departments you could have an interest in instead.