I installed Service Desk Server because I wanted to use it as a Help Desk, mainly because of the (public) knowledge base and that isn't possible. So my solution is not to use Service Desk and only use Confluence with the Scroll Viewport plugin (that I found after a search). Scroll Viewport is really useful.
There is no anonymous access to Service Desk, as you've to have a contact to tell that the issue/bug/problem/request is solved. You cannot do this, if you don't know how to contact someone, as he is anonymous. What you can do, is allowing everyone to register himself in your service desk. The person that leaves his email address (is not anonymous anymore) & can create issues & be contacted, when solved.
Anonymous access in Jira Service Desk Cloud is possible by default. Instead of logging in with your account, there is a mandatory field e-mail address in each request form which will be used to create the ticket and for the communication.
In Jira Service Desk Server, the following two apps enable anonymous access to the portal:
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