As soon as you don't just look at momentary values, but the change of CO2 concentration in the atmosphere the picture is a lot less rosy. Nature can adapt, but it operates in time scales that reduce all of human civilization to a tiny blip in the history of the planet. The current change is unprecedented and is much more akin to extreme events like meteor impacts or huge volcano eruptions.

Actually looking at how nature has been and is changing right now affected by human made climate change, we are clearly steering towards an extinction event, not an era "with more life". Extinction means death. A lot of it. It's not the first extinction event of its kind, but catastrophic nonetheless.

Will there be a recovery after a million years or so? Sure. Will there be anything resembling human civilization? No.