I'm not so pessimistic, there have been examples of global coming together in reasonable equity, although not so much recently.I struggle to think of an instance when the world has come together to jointly solve an international crisis. Climate change is no different. The following is a generalisation, but no less relevant for that.
The most recent example is covid - genuinely global with the capacity to affect every nation (and person) on the planet. Countries initially responded individually - lockdowns (Europe), denial (US, Brazil), shut borders completely (Oz, NZ), autocratic crisis management (China).
Then a vaccine is developed. Developed wealthy countries get the first supplies. Poorer nations are left to struggle - definitely second class citizens in the vaccine race.
In the context of climate change it is naive to assume that the community of nations will somehow see and act upon the mutual benefit of responding collectively and constructively.
Richer nations who consume more can afford to adapt and understand the benefits of so doing. Poorer nations cannot afford to adapt, fortunately they create low levels of greenhouse gas.
Wealthier nations will have tensions over how costs of adaptation and transition are funded. It will no doubt follow the approach taken for other societal stresses from a genuine "we are all in this together" through to "it's up to everyone to make their own arrangements".
Assuming climate change response will herald a new age of collaborative endeavour to solve a global problem is IMHO sadly misplaced. Whilst supporting cooperative efforts, we should prepare our own response if/when this proves ineffectual.
The Montreal protocol is the best example where CFCs were phased out rapidly. The rich nations bore the early brunt of the phase out, and allowed developing nations much longer to do so. There was also generous funding provided from rich nations to enable developing countries to adapt.
Gordon Browns debt relieve in 2007 at the G20 was a massive forgiveness of debt to developing nations. Both of these initiatives were pretty well aimed at a collective good.
Other institutions such as the Word bank, IMF, and GATT/ WTO had specific policies to enable developing nations to industrialise, although these were partly self-serving as they supported the post WW2 Bretton woods world order, but they did provide global stability for developing nations to thrive.
The problem with covid responses is due to the sheer suddenness of the crisis. Rich nations were taken by surprise and pretty well had to look after themselves first. The old maxim about parents and marriage is look after yourself so you can look after others is an analogy. Until the nations that can invent vaccines keep their populations safe its hard to justify policy to help others. As vaccine capacity expands and the immediate threat of death is removed I think we will see a generous role-out in quite a timely fashion. Even now, the bulk of the deaths is still in developed countries. Very few of the top death rates are developing countries, the UK, US, France Italy are near the top of the death rate list. In Sub-Saharan Africa, South Africa has about half the death rate of us. Even taking into consideration underreporting in developing nations, Europe, North and south America have been hardest hit. The virous will, in time, start to devastate Africa, but hopefully vaccines will be flowing by then. In previous crises the world has come together to tackle Ebola outbreaks etc. There is a lot of self interest in averting global crises for all.
With climate change there is time to reach some form or consensus/equitable solution. There are a lot of vested interests to address such as the gulf nations, the industrial nations emerging nations, low lying countries, so its complicated and will be a messy process but I do think we have the capacity to act together.
A thing to worry about is the old American /western order is crumbling. With a dominant China with its different agenda and a very disruptive Russia with an agenda of causing maximum chaos it may be a lot tougher than past crisis management. Putin has publicly relished climate change. But China is very vulnerable to climate change so may well act as a catalyst and positive force going forward.
So whilst its generally a difficult and pessimistic situation, I don't think history has been that bad a president and there is just about time for collective self interest to kick in.