The tie-in world is huge and hugely complex.
Not only have series of novels based on characters been done but many argue that it is so overdone as to be destroying the field of f&sf (because talented newcomers find it more profitable to crack out a quick tie-in “tied” to a bigger name than to take the time to create a career based on their own original works).
You can find dozens of examples of big-name authors (or their heirs and estates) licensing others to create books in their universes: Isaac Asimov and Roger Zelazny are two that jump to mind.
There are even more books in which the big name lends a name to work that may be a true collaboration or more likely a book written from notes or an outline or nothing at all. Anne McCaffrey and Andre Norton’s collaborations are examples.
Baen Books likes to take its new authors and have them collaborate with bigger sellers to get their names out into the public. These will usually be in original series but may be related to or offshoots of ongoing series.
This is true in the mystery world as well. Both the Nero Wolfe and James Bond characters were continued by other authors. And of course there are orders of magnitude more Sherlock Holmes stories today than Conan Doyle ever wrote.
My guess is that there are hundreds if not thousands of examples of books based on print book series.
It’s simply way too early for Rowling to think of this and she is likely to deny others to play in her very personal world. But never say never. There were plans recently to continue C. S. Lewis’ Narnia series so who knows what might happen after she dies?