Forms with type=search, type=search2, and type=fulltext are used for search which corresponds to the "search" ARIA role (see MDN). The suggestion is to add role="search" to the form element for them.

Context
Of all things ARIA, InputBox currently supports only the aria-label attribute on the <input> element added in T242354:

Open questions
A possible concern here is that when several elements on the page share the same landmark role (like search or form), it is advised that they have different aria-labels. Currently the main MediaWiki search functionality has no aria-label parameter (I checked Vector 2022, Vector, Monobook), and InputBox only supports aria-labels on inputs, not the whole form. But I'm not sure that the users of assistive technologies really need any hint that the first search landmark on MediaWiki sites is the sitewide search. According to this note on MDN,

labels can be announced by screen readers together with the role. So does adding "Sitewide" to "search" really add value here?.. Another question is whether aria-label on forms created by InputBox is required.