I believe only internal links are rendered in the edit summary, so external links would still have to be normal text.
https://en.wikipedia.org/wiki/Help:Edit_summary#Edit_summary_properties_and_features

I can confirms this. External URLs cannot be transformed into links. This can easily tested when using the Preview on edits. You will get an preview of the edit summary as well.

Ok I just realized that interwiki links are possible. See this screenshot from commons and a file from English Wikipedia:

So this task is could be done. I would increase the story points though, since we need to build something ( or find something ) to construct these interwiki links.

I started looking into this some more and fiddled mostly with my local setup to make this testable and reproduceable. While doing that I realized one thing:

Creating interwiki links with [[]] and the parser does not work with more than one dimension of interwiki-ness. This means, when linking on Commons:

• [[wikivoyage:de:Paris]] will not bring you to https://de.wikivoyage.org/wiki/Paris but will create a link to https://en.wikivoyage.org/wiki/de:Paris
• [[de:wikivoyage:Paris]] will not bring you to https://de.wikivoyage.org/wiki/Paris but will create a link to https://de.wikipedia.org/wiki/wikivoyage:Paris

What that means:

• only the first part of a link can be interpreted as interwiki prefix pointing to hard coded lists of wikis
• by default language-code-like strings point to the corresponding language page of the project
  • for projects without language sub projects that always seems to be Wikipedia
  • [[de:TITLE]] will link to the German Wikivoyage page with TITLE when used from Wikivoyage
  • [[de:TITLE]] will link to the German Wikipedia page with TITLE when used from Wikipedia / Commons / Mediawiki / Meta
• generally a list of codes exist to point to other projects, if these are multilingual the links mostly go to the English version
  • [[w:TITLE]] will always link to the English Wikivoyage page with TITLE
  • [[wikivoyage:TITLE]] will always link to the English Wikivoyage page with TITLE
• a list can be found here https://en.wikipedia.org/wiki/Special:Interwiki these lists vary per project

So when importing files from Wikipedia to Commons in the Wikimedia setup we can indeed point to the specific file with [[LANG:FILE:NAME]], but when importing from other projects that have multilingual sub wikis that won't work.

The question now would be: Do we want to have the short special links for Wikipedia or do we rather want to go for the full URL so we have it identical for all cases? @Lea_WMDE

Thanks for the research, @WMDE-Fisch! I would say, let's just go with the full URL for now, and keep the work small.

In T189196#4161213, @WMDE-Fisch wrote:

So when importing files from Wikipedia to Commons in the Wikimedia setup we can indeed point to the specific file with [[LANG:FILE:NAME]], but when importing from other projects that have multilingual sub wikis that won't work.

Using link like [[wikt:de:Paris]] on Commons seems to bring me to the right place (German Wiktionary), eventhough technically it's redirected via English Wiktionary. That kind of links seem to be used for edit summaries for imports done via Special:Import already, e.g. here. Is that problematic?

Now this concerns log comments too.

I note that page titles in wiki links for revision imports (e.g. here) are not encoded. So doing the same here would also improve readability and for some cases save considerable amount of space (e.g. for this file import), besides making navigation easier.

And now there are also URLs in source wiki edit summaries (T227358). In addition to edit summaries and log comments on target wiki, those would also benefit from clickable wikilinks. Does that warrant a separate task?

The original request is about filenames in the edit summary. So the link will always be [[:c:File:<name on Commons>]]. The benefit of a clickable wikilink is that it is much faster to navigate to the new location. Personally I have never thought the long edit summary was a problem but I can see the benefit of a wikilink I can click on. (I just realized that this is an old ticket. I thought it was related to one about making edit summary shorter on source wiki)