This is definitely something that could be solved with Stack Exchange moderation tools. Questions could be moved to the appropiate site, the same way you'd move issues between GitHub repositories.
Not quite. It's impossible to move a question from Stack Overflow to Server Fault or Super User right now, you can only say that it might belong there.
Do you specifically mean "right now" ? As in it has been disabled at the current moment? Because there are plenty of questions that have been moved around from one site to another in the past.
That's great! I thought their issue was that questions are marked off-topic without further handling, requiring users to ask again on a different site.
Does this break links and lead to link rot? Other StackExchange sites don't seem to have the page rank of StackOverflow. It also makes it harder to restrict searches to a particular site when questions are spread across multiple sites inconsistently depending on what year they were asked.
That is already a thing the sites do.