These skins (among others, [[https://codesearch.wmflabs.org/search/?q=UseTwoButtonsSearchForm&i=nope&files=&repos=|non-WMF deployed]]) make use of this variable to provide two-buttons search form (see https://www.mediawiki.org/wiki/MediaWiki?useskin=monobook).
This variable (which lives in core but not used there) will be removed in T42622. It's On by default MediaWiki setting, so probably a large number of users are accustomed to what it provides, especially given the fact that there's no way they could have turned it off.
This task is to decide the future of the config option in these skins. If it's decided that any of these skin want continue supporting it, then the config would be moved inside the skin itself. Otherwise it would be removed completely.
[x] Monobook (show both buttons so no UI change on https://en.wikipedia.org/?useskin=monobook)
[x] Modern (show both buttons so no UI change on https://en.wikipedia.org/?useskin=monobook)
[] CologneBlue (show both buttons so no UI change on https://en.wikipedia.org/?useskin=monobook)
[x] Nostalgia (this skin will maintain the behavior without the config).
[x] Other skins (advised to move the config inside the skin itself if they want keep the behavior)