Have you explored the reports on the admin dashboard? Discourse collects quite a bit of data that you can use to measure the success of your community, such as daily active users. You don’t have to ask your users.
But if you really want to, you could embed a third party survey in the header using a theme customization. If I recall correctly, I think forum.asana.com used to have this but I just checked but it is no longer present. You could ask them how it worked out for them.