74:                                     // A collapsible element may have been added
75-                                     $( '.mw-identical-title' ).makeCollapsible();

Maybe this needs to be replaced with the hook? And figure out why it isn't always working.

Sorry, I didn’t check every situation. After some more testing (and using the source look), it’s obvious what happens: {{Identical}} works, because it has mw-identical-title class, but {{Related}} doesn’t (in no case, regardless of how the user got there), because its class is mw-related-title. I think relying on on-wiki classes or any other user-generated content is a Very Bad Thing, and should be avoided if possible. (For example it at least partly works on translatewiki, but doesn’t work at all on WMF wikis.) Here it seems possible with the MediaWiki hook, to which $messageDesc from line 63 can be passed. (I haven’t tested it on a local MediaWiki install, only using the browser console on translatewiki and Commons, where I used $messageDesc = $( '.infocolumn-block .message-desc' ). It’s not the same, but pretty similar, so I think it should work with the code in the extension’s module as well.)

Change 583039 had a related patch set uploaded (by Nikerabbit; owner: Nikerabbit):
[mediawiki/extensions/Translate@master] TUX: Use mw.hook( 'wikipage.content' ) for message documentation

https://gerrit.wikimedia.org/r/583039

Change 583039 merged by jenkins-bot:
[mediawiki/extensions/Translate@master] TUX: Use mw.hook( 'wikipage.content' ) for message documentation

https://gerrit.wikimedia.org/r/583039

Related patch has been merged.

This has been deployed to translatewiki.net and can be tested there.

For example, here on the yellow background color is [expand these messages] link generated by Template:Identical, which should always work after this fix.

Simlarly for Template:Related, on blue background: