Say humans found a way to exponentially increase the capability of plants to grow. Is it possible for it to cause an environment that can cause oxygen toxicity in humans?
Studies show that 0.5 bar of oxygen can be tolerated indefinitely.
The current partial pressure of oxygen in the atmosphere is 0.2 bar, so to go beyond that threshold the oxygen level should rise of more than 250%.
Apart from the lack of that much oxygen in the atmosphere, consider also that more oxygen in the atmosphere and a lot of vegetation means higher chances of fires and more sustained fires.
Fires of course would produce CO2 and consume O2, shifting back the equilibrium.
The reality is that, due to the high reactivity of oxygen, it's really difficult to have it unbound in large amounts.
The scenario you're describing has occurred in the past, at least in the sense that O2 levels have been much higher than they are now. They were at their highest levels during the Carboniferous period about 300 million years ago, at 35% compared to 20% today.
This isn't high enough to be toxic to humans, and in fact the result was that all forms of life were able to grow much, much larger. Insects in particular were colossal compared to today, and it was the O2 levels that permitted that.