I am sure everyone knows, but just in case, XSS relates to inputing <script> tag which would then be executed and do bad things.
I tried to put in this script as username:
<script>alert('hello');</script>
It did not execute but left that code intact in the html. I think that is why vulnerability is reported.
So agreed, looks like false positive.
Same for search box...
I think as soon as input is received, it should be stripped of html tags, and such tags would never be shown in any form. That is easy to do. Such tags make no sense for user input or search input.