Ah, Apophis, nice one. I cannot but marvel at your and some other poster’s unwaivering optimism. I recall you had a similar attitude when we discussed Covid almost a year ago - and so did I, my guesses concerning the number of deaths at the end of the year were much higher than yours. Must be a personality trait. So I am not going to convince you that the impact would be much worse than you hope, just as you are not going to convince me that surviving as a species is almost a given. I wrote a book about 15 years ago, unfortunately in German, so I can not show it to you in any meaningful way (or do you understand German? Are you ready to go through a machine translator like Deepl.com?), the subject was airships (you mentioned them some posts ago, I loved it), extinction, Apophis (no, really! Chapter 47 and others), frogs, the seed vault in Svalbard you mentioned above (chapter 93), madness and pets (Chapter 64 and 65, and many more, it is a long verbose book - probably also a character trait.)If you care to have a look, it can be read for free here. I just mention that to show that we have similar interests, only very different approaches, and that I take you seriously.
Now for the things I see differently concerning our asteroid. I will try to be systematic.
So a meteorite is coming towards planet Earth. A big one, Chicxulub-event size, that is the premise in the OP, though we don’t really know how big that one was, so we may play with the numbers. There are two possibilities: we see it well in advance (years) – or it takes us by surprise (months or days). I’ll dismiss the second possibility because the OP asked about what could we do if, and if we see it too late there is nothing we can do.
So we see it looong before it hits the fan. Now we must either break it up or deflect it. (Spoiler: we can do neither. It sucks, but physics is cruel and mercyless. Please bear with me and just keep on reading). In case we don’t manage we will try to prepare as good as possible for the event and brace for impact.
First we try to deflect it. That is sensible, if it does not hit us at all, the problem is solved. Now let’s move an impactor between 6.82×10^15 kg and 1.28×10^16 kg (Wikipedia dixit, under Chicxulub impactor ). Lasers have been sugested: if you fire them from the ground the atmosphere scatters the beam (and the beam scatters the atmosphere and burns a hole in it), if you fire them from space there is no way to cool the machine if it is to be powerful enough.
I postulate that we have to move the biest 10,000 km (10^7 m) laterally, that is: 6,000 km Earth radius and a safety margin of 4,000 km. That is a small safety margin, but could be enough. What force do we have to apply to the body? That depends on how much time we have. Now I will be the optimist one: say we have 10 years time to apply a constant force and the means to do so (I will come back to the means in a moment). A year is the same as 31,557,000 seconds, ten years 315,570,000 s, that is about 3,2×10^8 s. What have we got? Something between (6.82×10^15 kg and 1.28×10^16 kg) times 10^7 m divided twice by 3,2×10^8 s, which is about between 666,000 and 1,250,000 kg m/s² (or Newton). Well, that is not that much! Only this force has to be applied every second, ten years long. Do you agree with this calculation? We have to exert a force of 1,000 kN on the body every second for ten years. How could we do this?
One option is with lasers, the other by detonating A- or H-bombs close to the body (which I will call Helen from now on, for reasons. Only known to my first wife and me). Let’s try:
Lasers: light does not exert a signficant force on Helen by itself, the idea is to melt and then boil away the mass necessary. If possible, in the right direction with the right velocity. 1,000 kN is the force of a mass of one metric ton ejected with a speed of 1 m/s. Every second. If Helen is made of ice (quite plausible, according to my experience) melting and blasting that material away heating one ton of ice to 0°C (actual temp out there: around -100°C, we are still beyond Jupiter if Helen needs ten years to reach us), and then some more to give the ton of water some impulse. That is at least 100,000 kCal/s to rise the temperature and 80,000 to melt it. To this we must add the laserlight reflected, that will depend on the albedo of Helen. That can be quite high for bodies made of ice. In fact, I would rather heat Helen up to boiling point (100,000 kCal more per second) and then boil her (540,000 kCal, the latent heat. Quite a lot). Am I right?
Now if Helen is made of iron, we will never be able to melt and boil to eject one ton every second, the numbers would be even higher (althoug the latent heat and the specific heat factor of iron is much lower, the temperature to reach is much higher. Melting point of iron: 1,535°C, boiling point 2,861°C. Plus latent heat. One ton every second! And I bet this darn Helen rotates, which makes heating her up as desired even more difficult. I am afraid we can forget this.
Atomic or hydrogen bombs? To eject one ton of material every second on average (the bombs will work on pulses: one explosion, one pulse, assume we get one every day to the very precise location and blast it, so that it manages to eject 1 ton times 60 times 60 times 24 = 86,400 tons in the right direction with the right speed – no mean feat) we would have to send almost 4,000 bombs to the right place, which in itself will consume some of the 10 years I optimistically assumed. Do we have 4,000 bombs and rockets for them? I doubt it.
So we will have to break Helen up (I’m starting to like this). I already calculated (see post above) that if we smash Helen to tiny pieces, so that all the energy is transfered to the atmosphere during entry (no pieces reach the ground) this would heat up the atmosphere by around 20°C, or 40°C if this happened only on one side. You objected to this second scenario because the Earth turns. Granted. But 20°C is catastrophic too. At least we would not need bunkers to hide, only refrigerators. And the energy to keep them going. No atomic energy is possible! Cite, cite.
If we only manage to break Helen up to pieces of around 80x80x80m we would have about 6,000,000 of them, which is 2,000x3,000, a number I have chosen because it probably is about the resolution of your computer screen if you have a good one. Take a world map, make it fit within your screen and imagine one meteor of that size falling on every single pixel. Than does not look like a good idea either.
Perhaps the best thing is to leave Helen intact and hope that when it falls the story of the dinosaurs repeats itself. Some places might be more protected, lucky or whatever and something would survive there. My guess is that if some of the energy is not turned into heat but used to make a crater, a tsunami, to heat the interior of the Earth the effects might be lighter.
But then humanity must brace for impact. And here is where I fundamentally disagree with your approach: we have left out psychology in our considerations. All of humanity must work together to save a few. Would the ones not lucky, or mighty, or ruthless enough to be saved actively work, and work well, for the benefit of the others? Would you work carefully and honestly to save me, for instance? And save the kind of people who would elbow their way into the saving list too? People like, say, Jeff Bezos and Mark Zuckerberg and the crown prince of Saudi Arabia and Kim Kardashian? (and I haven’t listed the worst ones!) I for one can tell you: I would sabotage the whole endeavor if forced to work for them. And how would they force me if I was going to die anyway?
I think this post is already too long, so I am not going to dwell into why atomic energy is not the solution, but an aditional problem, especially if the atomic installations are not shut down properly and result in 500 Chernobyls after the impact, and what will happen with all the big dams like Assuan (bye bye, Cairo) and the Three Gorges Dam and the Hoover dam when they are not mantained for years full of earthquakes and so on.