The BBC report as usual simplifies things a lot, stating that Crossrail 2 will run from 'Cheshunt to Epsom'.
Describing various possible branches in detail would probably be considered a failure as their aim appears to generally dumb down their reports.
Most of their Crossrail 1 reporting over a number of years failed to describe that whole route as well, often reporting it as 'Maidenhead to Shenfield' (only). Even now they rarely mention Abbey Wood, and suggest services running from Berkshire via Heathrow, rather than from Berkshire and Heathrow...
Hence just don't take BBC descriptions to be accurate.
In principle Crossrail at only 24 tph could take the whole of the existing SWT slow line services through Wimbledon, and then add a few more. This has been discussed in earlier threads in this forum, it was thought that there'd be a few SWT inner suburban services into Waterloo, to cater for local flows e.g. at Earlsfield, but as described in the London and SE RUS, you'd basically get a four track railway for use of long distance services, with significantly more mainline services operating, with stops at Clapham Jn becoming the norm.
But that document also described a situation where the tunnel portal would be between Raynes Park and Wimbledon, suggesting that Crossrail would be in tunnel at Wimbledon, so having its own dedicated platforms. The RUS also mentioned six tracking on the surface inbound from New Malden, presumably to allow services from the Epsom and Kingston branches to Crossrail to run independently of the 4 SWML tracks.
Seems there's loads of detail to be worked out, and really it is just far to early.