During the Paleogene, the terrestrial plants and animals were very different from those of today.
Now on all continents and islands most of the big animals and plants are humans, domestic animals and cultivated plants. The wild animals and plants, even if they are much more varied, with many thousands times more species than the domestic ones, are much smaller in quantities, with only a few kinds that are non-negligible, e.g. ants, termites, rodents.
So if we will return in a short time to the Paleogene climate, the main question is how this will affect the few dominant animal species, like chicken, humans, pigs, sheep, cattle, dogs and the main cultivated plants, all of which are not adapted to a Paleogene climate and which will not be able to adapt in such a short time.
It is likely that places like Canada, Alaska, Greenland, Siberia, Antarctica might become nicer places where to live and practice agriculture, but the few people who live now there would not welcome invaders coming from places that are no longer habitable.
I don't see that everything except Canada, Alaska, Greenland, Siberia and Antarctica was inhabitable. For instance in Eocene the climate remained fairly warm and homogeneous (the most uniform in the Cenozoic).
From the equator to the poles, forests grew. Fossilized remains of cypress and sequoia have been found on the Arctic Ellesmere Island, and palms — in Alaska and northern Europe.
Equatorial and tropical forests (with palms, fig trees, and sandalwood trees) persisted in Africa, South America, India, and Australia.
Eucalypts, sequoias spread widely, and new types of broad‑leaved trees appeared.
By the end of the Eocene, rainforests were preserved only in the equatorial parts of South America, Africa, India, and Australia — due to the onset of cooling.
The only outcome is advanced human civilization will go extinct, with the carrying capacity of the world to support enough humans to specialize. Maybe that's the AI rush and drive to distract everyone with divisive presidents and pointless wars.