Super hacky sketch of an improvement:

diff --git a/includes/Linker.php b/includes/Linker.php
index 8ebbd1c19e..33c5e9432a 100644
--- a/includes/Linker.php
+++ b/includes/Linker.php
@@ -120,7 +120,15 @@ public static function link(
 			return $linkRenderer->makePreloadedLink( $target, $text, '', $customAttribs, $query );
 		}
 
-		return $linkRenderer->makeLink( $target, $text, $customAttribs, $query );
+		if ( in_array( 'comment', $options, true ) ) {
+			$linkRenderer->renderingComment = true;
+		}
+
+		try {
+			return $linkRenderer->makeLink( $target, $text, $customAttribs, $query );
+		} finally {
+			$linkRenderer->renderingComment = false;
+		}
 	}
 
 	/**
@@ -1639,6 +1647,7 @@ public static function makeCommentLink(
 				/* escape = */ false // Already escaped
 			);
 		} else {
+			$options[] = 'comment';
 			$link = self::link( $linkTarget, $text, [], [], $options );
 		}
 
diff --git a/includes/linker/LinkRenderer.php b/includes/linker/LinkRenderer.php
index 18df8cfbdd..65a1c02baf 100644
--- a/includes/linker/LinkRenderer.php
+++ b/includes/linker/LinkRenderer.php
@@ -82,6 +82,8 @@ class LinkRenderer {
 	 */
 	private $specialPageFactory;
 
+	public $renderingComment = false;
+
 	/**
 	 * @internal For use by LinkRendererFactory
 	 * @param TitleFormatter $titleFormatter

diff --git a/repo/includes/Hooks/HtmlPageLinkRendererEndHookHandler.php b/repo/includes/Hooks/HtmlPageLinkRendererEndHookHandler.php
index 9718c45db1..0967aa7004 100644
--- a/repo/includes/Hooks/HtmlPageLinkRendererEndHookHandler.php
+++ b/repo/includes/Hooks/HtmlPageLinkRendererEndHookHandler.php
@@ -169,6 +169,10 @@ public function onHtmlPageLinkRendererEnd(
 			return true;
 		}
 
+		if ( !$linkRenderer->renderingComment ) {
+			return true;
+		}
+
 		return $this->doHtmlPageLinkRendererEnd(
 			$linkRenderer,
 			Title::newFromLinkTarget( $target ),

This seems to work locally. A non-hacky version will look somewhat different, of course, but I think it might not be totally separate either. Looking at the many methods in Linker/LinkRenderer, and how edit summary links and regular links share so much code, I feel like a separate hook handler (which would be a very clean solution from Wikibase’s point of view) might not be feasible; some kind of flag on the link renderer, where the hook handler can look up what the link renderer is doing, could be a relatively economical way to transfer this information between Linker::makeCommentLink() and the hook handler. (The flag wouldn’t necessarily need to be mutable: Linker::link() already creates different LinkRenderer instances for different $options, so there could also be “a link renderer for comment links”, and the flag of that instance would never change during its lifetime.)

It turns out the implementation of comment link formatting was recently changed, and Linker::makeCommentLink() is gone (T285917), but I think I still found a solution that’s not too ugly.

Change 726638 had a related patch set uploaded (by Lucas Werkmeister (WMDE); author: Lucas Werkmeister (WMDE)):

[mediawiki/core@master] Add comment flag to LinkRenderer

https://gerrit.wikimedia.org/r/726638

Change 726639 had a related patch set uploaded (by Lucas Werkmeister (WMDE); author: Lucas Werkmeister (WMDE)):

[mediawiki/extensions/Wikibase@master] Only add labels to entity links in comments and special pages

https://gerrit.wikimedia.org/r/726639

Change 726638 merged by jenkins-bot:

[mediawiki/core@master] Add comment flag to LinkRenderer

https://gerrit.wikimedia.org/r/726638

Change 726639 merged by jenkins-bot:

[mediawiki/extensions/Wikibase@master] Only add labels to entity links in comments and special pages

https://gerrit.wikimedia.org/r/726639

No train this week (because of veterans’ day, I assume?), so we won’t be able to verify it until the end of next week. Do we want to try backporting to wmf.7? (But maybe not quite yet, T293948 is in a bit of a precarious state if I understand correctly.)

In T292203#7489604, @Lucas_Werkmeister_WMDE wrote:

No train this week (because of veterans’ day, I assume?), so we won’t be able to verify it until the end of next week. Do we want to try backporting to wmf.7? (But maybe not quite yet, T293948 is in a bit of a precarious state if I understand correctly.)

If T293948 gets better and an opportunity to backport presents itself, then let's try backporting. But we don't have to force it. This was broken for so long, waiting a week longer won't make that much of a difference either.