I'm using MW 1.26 with Lingo installed (via composer) and HeaderTabs is working for me. (e.g. https://freephile.org/wiki/MediaWiki/Auth). The page says it doesn't work with Lingo. I didn't want to edit the page based on a sample size of 1, but perhaps the incompatibility is a thing of the past.
Also, one quirk I noticed is that I had to explicitly add __NOTOC__
on a sub-page despite the default / explicit
$wgHeaderTabsDisableDefaultToc = true; // default true
in LocalSettings.php