You may want to narrow your focus a bit as the Americas are not only very forested, but also have some pretty distinct regions who would have interacted with the world differently. I am not able to speak on it, but there was some interesting interactions in the Amazon that may have had lasting impacts.

In the Eastern Woodlands we see a heavy usage of the woodland ecosystems by the cultures living in and near them. But was it logging? Forest management? Hard to say, but I would argue it wasnt, or at least not at a level you list. But there are lots of sites where we see a detrimental effect on the local ecosystem by humans using resources from the woodlands. Espcially wood for fires and construction, I know at Cahokia we can see this effect in how far people have to travel to obtain their timber. The woods would have been pushed further and further back as people harvested it, so overtime you would have seen an impact in certain areas. But this would have been a drop in the ocean when compared to how vast the woodlands were. So they would have influenced the forests, but this would have been within the ability of the ecosystem to recover over time.