Would a global catastrophe unite or divide nations?

It heavily depends on the nature of catastrophe.

* meteor coming to earth in 20 years, obliterating everything - the humanity will unite

* gradual reduction of temperature by 20 degrees. Every nation for themselves.

Yes, as long as it is indisputable. If there is any question as to how real it is then doubtful. See climate change.

i.e. meteor on 100% collision course...yes. 5%...less confident humanity will pull together

Spoiler for The Watchmen:

The Watchmen has two examples (comic and movie) that I thought might work, if they were really pulled off.

However, even then I agree with the other comments currently posted that there would still be deniers, who would ultimately win.

Maybe humanity could pull it off, but if they could I'm not sure we'd be able to sustain it.

We're good at short term disasters, but not at preventing them, or following through with the lessons we've learned.

Historically, war has been something where a truly large number of people and a large fraction of world economy could be "united". It's hard to imagine a disaster that would require the same level of both world GDP focus AND individual human labor participation in the modern economy. COVID seems the best example, but the GDP impact seems to have been largely negative in the sense of needing more factories to (temporarily) close more than new production to come on line. I'm quite curious to hear brainstorms of acute disaster scenarios that would drive a big transition of production to something special...

Look at the response to COVID-19.

“Cannot swords be turned to plowshares? Can we and all nations not live in peace? In our obsession with antagonisms of the moment, we often forget how much unites all the members of humanity,” Reagan said.

“Perhaps we need some outside, universal threat to make us recognize this common bond,” Reagan proposed.

“I occasionally think how quickly our differences worldwide would vanish if we were facing an alien threat from outside this world. And yet, I ask you, is not an alien force already among us? What could be more alien to the universal aspirations of our peoples than war and the threat of war?”

There's a great YouTube channel that goes deep into questions like these.

[1] https://www.youtube.com/@WhatifAltHist

Yes and no. Some dedicated individuals and groups will come together and try. And the power struggle within will bifurcate the effort, as all human collective efforts tend so have internal power struggles. Those losing in that power struggle will look to the deniers of the need for the collective effort and with luck manipulate that population to "join" them. ..and of course, as we play our political games, the clock runs out and a few might survive.

Who caused the catastrophe?

the two examples we hear are - meteors with 100% certainty of hitting - climate change

I'd like to hear opinions on other thing. would nations unite against alien invasion? a solar flare? killer robots?

Are economic interests in place? Good luck with that.

You mean will.

I don't really see benefit for countries like Japan, Australia or other isolated countries to join others.

Scott Adams talks about the law of slow disasters and thinks that cooperation against a common threat is possible, as long as there is enough time to prepare and agree. Eg. working around climate change will happen, shooting down the next meteor will not.