I think that it will be easiest to have a special page or an extension, different view of "Special:Version". @Legoktm suggested a script doing the job however in this case one would need access to the hosting environment to run it. There are cases in which the hosting environment does not allow running a scrip easily. I do not think that this is good since it also requires an extra effort in logging in etc.

So, basically, you want the information from Special:Version as raw text. For articles, there is action=raw to view the contents as raw text. So extending that thought, we could add action=raw to Special:Version and either add a tab to the page or a link in the toolbox.

Markdown and Remarkup (Phabricator) differ too much from wikitext that there isn't a single solution template possible; at least not one that includes a header. All three languages do support * for lists. Wikitext and Remarkup support using equal signs for headers and Markdown and Remarkup both support using pound signs for headers. In that case, the template could be

== Setup ==
* MediaWiki - 1.29.1 (a69ecd8) 18:59, 23. Aug. 2017
* PHP - 5.6.30-0+deb8u1 (apache2handler)
* MariaDB - 10.0.32-MariaDB-1~jessie
* ICU - 52.1
* LuaSandbox - 2.0.13-alpha
* Lua - 5.1.5

for Wikitext and Remarkup. Perhaps another parameter could be added to set the output format to Markdown? - Or use a parameter to output to Wikitext, defaulting to Remarkup and Markdown.

So extending that thought, we could add action=raw to Special:Version and either add a tab to the page or a link in the toolbox.

Indeed, this was my original idea and I still like it.

Or use a parameter to output to Wikitext, defaulting to Remarkup and Markdown.

Perhaps just providing links/buttons to select and get to the desired output markup.

I think dropping the header for now and outputting a common syntax that works with both wikitext and remarkup sounds good to me.

In fr.wikisource.org with 10.0.32-MariaDB which differ from 10.0.31-MariaDB in www.mediawiki.org,
I get and error, 10 minuts after a good run:

• Erreur Lua dans Module:Central-s-fr à la ligne 1709 : attempt to index global 'wikibase' (a nil value).

@Rical I am pretty sure you are on the wrong issue here. It looks to me like you should first conact the creator of the module in question.

About the date-time data like " 18:59, 23. Aug. 2017 " is not so easy to adapt in any other format. ( But it could continue if needed for someone. )
In understanding, an UTC date-time could be better, like in present Special:Version dedicated page. Example:
MediaWiki * 1.32.0-wmf.26 (rMWa9add8941f8d) * 2018-10-17T20:29:05
Thanks in advance from coders for this easier format.