Why Corbyn's second referendum announcement changes everything – even if he's still lukewarm

Qualified, tempered, cautious. As ever with Jeremy Corbyn and Europe, his announcement that the Labour Party would support a new public vote on Brexit is not straightforward. Yes, Labour would support a new vote, but only after it has put a motion on its own Brexit plan forward for a vote in the House of Commons.
Is this a genuine attempt, to take Corbyn at his own word, to stop a chaotic, Tory Brexit? Or is the announcement actually a cynical ploy to get at least some form of Brexit through the Commons? Remainers despairing at Corbyn’s handling of Brexit could be forgiven for worrying that it could be the latter, and the mixed messages coming out of the Labour Party HQ would not have settled the nerves.