- MediaWiki 1.31+
This is a feature request for MediaWiki core though this will also help extensions. Earlier versions as indicated above do not have this feature either however I am just mentioning supported versions of MediaWiki here.
While it is possible to set namespace to be searched by default with $wgNamespacesToBeSearchedDefault it is not possible to set a default for the search tabs/sections to be shown by default. Thus having some method (e.g. hook) in  to set a default profile would made things easier for users and administrators and moreover also allow extension defined tabs to be set by default - not just MediaWiki core.