Trying to understand the problem, my first thoughts are:
Why is there a copy, and why can that copy (technically) become out of date?

I edited the description, hoping it's a bit more clear now. There's a lot of documentation on wikis, so it makes sense that also product/feature documentation lives there. I guess the community feels it like something they own and can customize how they want (for example, they may want to add their own navigation templates, or they may want to change the design so that it reflects other help pages, etc.). They probably also feel more free to discuss any changes in the talk page in their own language, which is something I don't see much at mediawiki.org. Finally, mediawiki.org provides generic documentation, which is not tailored on how software works at a given WMF project (it frequently includes instructions about configuration stuff at non WMF wikis, which may confuse a reader/editor of our sites), and doesn't really address the issue of wide understandability. As an example, the VE user guide at en.wiki currently features instructions for Citoid (which is enabled there, but not on most wikis), which are missing on mw.org instead.
Usually though, after a first version of a page is created locally (be it a partial or a full translation of content on mediawiki.org), it may live on the wiki unchanged for years, unless the community has a taskforce dedicated to maintaining this kind of content. This issue is particularly evident for VE "portal" pages (these ones), and especially at small wikis.

My first thought is still the social part instead of the technical part:
What is the motivation of people who create localized copies of the VE user guide, if the translated canonical page is available and could be redirected to?

For example the German one says that @JanWMF created the page.
@JanWMF: Please share your intentions and enlighten me. Thanks. :)

I think I did cover that in my comment: it mostly boils down to https://meta.wikimedia.org/wiki/Not_my_wiki and to a wider engagement of the local community, if work around documentation pages is done locally.

As a data point, compare views for VE's user guide at mw.org and at en.wp.

T91162: RFC: Shadow namespaces can help to solve that problem, by displaying the centralized doc instead of a localized one.

In T96875#1488572, @Elitre wrote:

As a data point, compare views for VE's user guide at mw.org and at en.wp.

Updated/working links: mw.org and at en.wp
And the German example: mw.org and at de.wp
And a French example: mw.org and at fr.wp

Beyond the issue of one page being out of date, there's also the sisterproject issue of "which do I copy from or redirect to?" E.g. the French Wikipedia's guide is quite different from the French translation of the Mediawiki version, so how would the French Wikivoyage decide which to copy from or redirect to?

I too, hope that shadow namespaces will help (at least partially) resolve this in the future.

Is anyone planning to work on this task during Community-Relations-Support (Oct-Dec-2016) (or Community-Relations-Support (Jan-Mar 2017) )?

Adding I18n with the hope that this brings more attention to this idea.

This isn't actually something for us. This is about a popup or something being displayed at mw.org or on the local wiki that warns "the equivalent of this page at ... was last updated on ...". Or we could just slap a more prominent warning on all docs pages that an equivalent elsewhere exist, check it out.

Right now, if it's not us who pushes this request, then probably nobody else will.

Let's see. I wonder whether Lua magic (or magicwords?) actually allows this:

• Given a page title in another wiki, retrieve the last modification date of that page.

If that is possible, then a template with some smartness would be possible. It could compare the date of the local version vs the mediawiki.org version (or vice versa) and act accordingly.