Both are unused outside core:
https://codesearch.wmflabs.org/search/?q=SkinTemplatePreventOtherActiveTabs&i=nope&files=&repos=
https://codesearch.wmflabs.org/search/?q=SkinTemplateTabAction&i=nope&files=&repos=
Let's deprecate them immediately rather than support hooks that add complexity to skin rendering.
Developer notes
Hooks are how extensions integrate with mediawiki. They can also be registered in LocalSettings.php like so:
$wgHooks['SkinTemplatePreventOtherActiveTabs'][] = function ( &$skinTemplate, &res ) { $res .= 'hello world!'; };
For the purpose of this task I suggest understanding how they hooks work and what they do, and then confirm that when marked as deprecated a deprecation warning shows up in MediaWiki.
Use
`
$wgDeprecationWarnings = true;
`
to show deprecation warnings.
Note: https://lists.wikimedia.org/pipermail/wikitech-l/2020-June/093461.html has some notes on how the deprecation process now works. It recently changed so don't rely on the code too much.