The DOM node of search entry accessible has @id="q".
The "Search" label for HTML input is placed over it (absolutely positioned), when I click on the label then it doesn't focus the HTML input. So the problem is not in a11y. Moving into more appropriate component, however I'm not sure it's 100% correct.
Could this be a problem? <li><a href="#q">Skip to Search</a></li>
mozilla.org has changed significantly... is this still an issue? If so, can you provide a testcase?
I don't see any searchfield labels anymore, closing the bug