Umm... - Smallpox eradication was a global effort. - Polio eradication was a global effort.(unfortunately delayed by religious fanatics in a small number of countries)
Also it’s worth noting that the vaccines were already years into development before COVID hit. We knew there was a risk of a Coronavirus outbreak (by virtue of the fact that we had dodged two Coronavirus pandemics a decade earlier). Granted the increased funding and urgency of COVID helped speed things along; but they weren’t exactly starting from scratch.
So it’s still not really clear how we would cope with a more dramatic or unknown situation.
What I did learn about the pandemic was normal folk will completely disregard their own safety just to stick a middle finger to the government. Which is not only concerning for the future survival of our species but also a direct contradiction to your point about civilisation banding together.
In a matter of just three years we rethought how we work, live, travel, and socialize. The global community came up with a vaccine in an extraordinarily short amount of time, and then coordinated a roll out.
We've seen how humanity can adapt at scale when we are motivated. I don't know what answer we will have to the ecological ruin we have layed out. Maybe we don't have an answer to it, that will be a truly humbling moment.