It’s not specific to Vector 2022. I tested all seven skins available on WMF wikis, the results:

• Vector 2022: broken
• Vector 2010: works
• Monobook: broken
• Timeless: broken
• Modern: broken
• Cologne Blue: broken
• Minerva: traditional preview doesn’t show language links either

So it’s more like an incident that Vector 2010 does work. It looks like live preview makes assumptions about how language links work that hold only in Vector 2010, not even in its closest relatives (Monobook and Modern). I think this is the point where a new API should be introduced, e.g.

/**
 * @param {{href: string, bcp47: string, nativeName: string, tooltip: string}[]} links
 */
mw.util.replaceLanguageLinks(links) {...}

…which can (and should) be implemented by each skin on its own, putting the language links where they belong on that particular skin.

In T367657#9905597, @Tacsipacsi wrote:

It looks like live preview makes assumptions about how language links work that hold only in Vector 2010.

This is correct. There was no predictable layout (no API contract) in live preview for most elements, so traditionally almost everything that wasn't the actual wikitext would not render. At some point I improved live preview to support more elements, but several of these were only supported on Vector (2010) and it very much depends on the HTML layout.

There has been no effort yet to define a contract for how language links would update in preview

In T367657#9906302, @TheDJ wrote:

There has been no effort yet to define a contract for how language links would update in preview

Except for my proposal above (granted, it wasn’t that big of an effort…). Is there an official way to propose and discuss such APIs? Given that all skins are expected to implement it, which makes it very hard to fix it afterwards if we get it wrong for the first time, I don’t want to take it light, but I’d like to get it rolling. (And if we’re at it, maybe categories could be fixed as well – they’re currently broken on Timeless because live preview doesn’t account for the fact that Timeless renders categories at multiple places to make the show them at different places at different screen resolutions.)