Right now there are no real updates. Transport for London (TfL) have put a business case for Crossrail 2 to the Government, but it has not been confirmed/approved. The scheme was missing from the Conservative election manifesto and the Queens Speech, which may or may not mean anything. And the Transport Secretary Chris Grayling rather dislikes mayor Sadiq Khan, which may or may not mean anything.
There was a leak of a document recently in City AM, where the route was via Tooting not Balham and dropped Chelsea, but after querying, it was established that this was a route for the purpose of calculating numbers, not a final decided route.
As such, all everyone can do is wait. At some point, someone will have to make a decision!