That's documented and probably expected behavior (if it still makes sense is another question). The page says:

The “http://” protocol specification is optional; any other protocol (“https://”, etc.) must be given explicitly.

In T221438#5125041, @Aklapper wrote:

That's documented and probably expected behavior (if it still makes sense is another question). The page says:

The “http://” protocol specification is optional; any other protocol (“https://”, etc.) must be given explicitly.

The documentation of this limitation seems to only exist on :en.
There is nothing on:

• https://de.wikipedia.org/wiki/Spezial:Weblinksuche
• https://fr.wikipedia.org/wiki/Sp%C3%A9cial:Recherche_de_lien

https://de.wikipedia.org/wiki/MediaWiki:Linksearch-text or https://fr.wikipedia.org/wiki/MediaWiki:Linksearch-text define the text on those sites.

Thanks!
The fact that it's not documented on Mediawiki itself seems to mean that it's not the expected behavior, meaning that the documentation on :en was added to avoid unexpected results.

Here's where http:// is used as default instead of both http:// and https://
https://phabricator.wikimedia.org/source/mediawiki/browse/master/includes/specials/SpecialLinkSearch.php$73

// Get protocol, default is http://
$protocol = 'http://';

After the externallinks migration (T312666) this should be rather easy to implement. I can take a look at it in the hackathon.