On 1.35, the core search suggestion module (mw.searchSuggest) is loaded through the page ready script when user focus on the search field. However, because of the change (T233676, T233677), there is no way to disable the module now, and as a skin author I'm unable to provide a custom search suggestion module without changing the class names of the search box. The search config from Desktop Improvements (T257706, T250851) didn't make it into the 1.35 branch.
Would it be possible to backport the search config from the master branch?
Master (with the search config check):
https://doc.wikimedia.org/mediawiki-core/master/js/source/ready.html#mw-plugin-page-ready-method-loadSearchModule
By the way the change was not recorded in the release notes.