Feature summary: There are a number of ways to go about this, but one would be something like a {{REQUESTEDPAGENAME}} magic word that tells you what page the user actually requested from the server. Currently this is shown to readers through "Redirected from ..." (and in the URL if they have JS off), but not made accessible to the parser at all, as far as I know. Some mechanism that could be placed on a redirect, the contents of which would display at the top of the target page to a reader who follows the redirect, but otherwise not. See T397999#10952836.
Use case(s): I am an editor on Wikipesija.org, a wiki written in Toki Pona. In Toki Pona, there are not definitive canonical names for most things, and this is seen as a feature of the language rather than a bug. To avoid the wiki becoming a de facto authoritative source, the wiki's sysadmin, @Tbodt, created Extension:MultiTitle. This works fine for now, but the wiki is in the process of becoming tok.wikipedia.org (currently marked as eligible by LangCom), and once it does, my understanding is we wouldn't be able to get that extension enabled on WMF servers without some WMF team taking on stewardship, which may be difficult to get for an extension used by a single wiki.
But this wouldn't just help our one wiki. All major wikis, AFAIK, use hatnotes, and one common form of hatnote is "X redirects here; you may have been looking for Y". On enwiki, we sometimes face disputes as to how to handle cases where a hatnote is technically valid, but very very obscure relative to the page's content—for instance, someone typing "Sultan of Swat" almost certainly meant Babe Ruth, and that term redirects to his article; but there's some small chance they meant the leader of the obscure Sultanate of Swat... but this link will be irrelevant to almost all of his article's readers. Many users think that the first thing a reader sees on an article shouldn't be a reference to another article they almost certainly weren't looking for. This change would allow a solution to that.
Benefits: For the Wikipesija.org community, which hopes to soon be the Toki Pona Wikipedia community, this would be incredibly helpful. It's an important part of our mission to not corrupt the subjectivity and context-sensitivity of Toki Pona, and the ability to show a user the title they requested, rather than implicitly saying "Actually here is the correct title", would be an important part of that.
This would significantly improve the display of "X redirects here" hatnotes on all wikis. In the example I gave above, we could have syntax like {{#ifeq:{{REQUESTEDPAGENAME}}|Sultan of Swat|{{redirect|Sultan of Swat|the title|Sultanate of Swat}}}}. But more broadly, {{redirect}} could probably be made to by default only display if {{REQUESTEDPAGENAME}} isn't {{FULLPAGENAME}}. There is rarely a reason to show it to people who accessed the page directly. See T397999#10952836.
There would be other benefits too. For instance, a user who redirects their bot's talk page to their own talk page could have a note visible only to people who were looking for the bot's talk page. There are also probably some applications for multilingual or multi-script pages on wikis where Translate isn't used. And many soft redirects that are used to caution readers about something (e.g. dewiki's "obsolete spelling" redirects) could potentially be converted to hard redirects, with the warning showing up conditionally at the target.