He has to approve. His only hope is some EU state objects but its unlikely.
Yes, Boris Johnson’s hands are tied.
The EU will approve the “Flextension” allowing Brexit to be delayed forever.
France made some noise that they would not vote for an extension, but I think that was kabuki theater. The EU needs the positive revenue from the UK, France and Germany to support the other members.
Remember, with a UK in the EU, there is more money for the EU to play with. That is the bottom line.
Boris does not have to approve. The only point of the Benn act was for him to ask. Nothing about him approving it. He can make excuses and delay and not ratify it.