>overall global forest cover has been increasing for about a century.
Can you cite a source for that claim? WRI's Global Forest Review data across the last 20 years shows annual primary losses between 2 and 6 million hectares with an upwards trend, and overall loss in the last 20 years sitting at 411 million hectares.
In terms of the longer view: "The turn of the 20th century is when global forest loss reached the halfway point: half of total forest loss occurred from 8,000BC to 1900; the other half occurred in the last century alone."
I remember being surprised to read about "global greening" - here are some links about it. I don't know if it's such an optimistic trend as presented though, and what it means in the context of large-scale deforestation that you mentioned.
Greening mitigates the impact of climate change to a point, but that we're seeing it so strongly take effect is alarming because it indicates how strong the underlying shifts are, and there comes a point that it ceases to mitigate the negative effects. As the equator becomes increasingly desertified polar regions shift from barren icescapes to being able to support more plant life. Also as photosynthesis increases due to greater CO2 in the atmosphere so too does plant respiration, where carbon dioxide is released back into the atmosphere overnight. One way to look at it - The entire plant biomass of the earth removes about as much carbon from the atmosphere each year as China alone emits in that same year. So the capacity here to mitigate climate change via global greening is quite limited.
Anything that acts as a damping mechanism on the impacts of climate change has to be taken as a good thing though - Our biggest addressable existential threat is the rate of change, and slowing that via any means is a good thing.
Carbon Dioxide Fertilization Greening Earth, Study Finds - https://www.nasa.gov/feature/goddard/2016/carbon-dioxide-fer...
Global greening is happening faster than climate change, and it’s a good thing - https://wattsupwiththat.com/2019/07/05/global-greening-is-ha...