Currently an editor on XXWiki cannot easily see an Event hosted on YYWiki.

What you can currently do is visit the respective EventDetails special page, e.g. https://meta.wikimedia.org/wiki/Special:EventDetails/4242 vs https://fr.wikisource.org/wiki/Sp%C3%A9cial:EventDetails/4242 vs https://it.wiktionary.org/wiki/Speciale:EventDetails/4242 etc. This will give you all the information on the event, including some limited event management possibilities.

In order to register, she needs to visit YYWiki.

I think there are two key observations here.

• The first one is that users can also register from the RegisterForEvent special page, which is an alternate frontend to the event page dialog that also does not require JavaScript and that can be deep-linked. For example, https://meta.wikimedia.org/wiki/Special:RegisterForEvent/4242
  • However, even though the page is available on all wikis (ex), registration can only be completed on the wiki of the event, due to restrictions with permission checking. That's a problem that would need to be addressed even before thinking about interface changes, but cross-wiki permission checks in MediaWiki are not really a thing (doable with workarounds such as internal HTTP requests, but messy).
  • There's also the argument that the special page is hard to find if you don't know about it. The only way to access it right now (besides knowing the URL), is if you middle-click the "register for event" button to open the link in a new tab, or when registration via the dialog fails (you get redirected to the special page because there we can properly display a localised error message). We have T316604 about adding links in EventDetails.

If the event ID is 123, I would like a local template like {{Event|123}} to display the Event on an arbitrary page or Wiki.

What exactly would that syntax display? You can transclude a local event page with that syntax as with any other page, although it won't display the registration header, and I'm not sure if we could or should fix that. And obviously you wouldn't be able to transclude pages cross-wiki.

We could make the EventDetails page transcludable, like Special:AllEvents is. That's more realistic. I suppose we would still want to only transclude basic information, not the entire special page, because that could be too expensive.

Even if registering cross-wiki is challenging, having the ability to load something like screenshot below (which is not available in the more detailed views of wiki/Special:RegisterForEvent/4242... the screenshot below would indicate to me there is a registration link, and also a live counter of event attendees.

And most importantly, I could make this visible in places that matter to users, like a high volume talk page, encouraging people to get info, before even clicking it.