Could it slow down the internet because the main routers would be busy with forwarding DDOS packages?
Similar - "the whole internet". These days, large parts of that are semi-isolated ( https://en.wikipedia.org/wiki/Great_Firewall ) in various ways. I would not bet on anyone being able include all of those parts in any DDoS.
I'd assume that any serious-about-cyberintel goverment could DDoS all the non-isolated parts of the internet...at least for at least a short while. If they really cared to.
But actors in that league do not play "because I can" games. What objective might such a government have, which could not be better achieved in other ways?