From the previous question, this disk is also extremely thin.
Thickness: the disk is very thin. Its thickness when compared with its altitude and diameter is negligible.
What you're asking, basically, is what would happen if we opened a giant, opaque sheet 1km high above the rain forest? I see two issues: sunlight and weather.
How Much Of The Sky Will It Cover?
A 40km diameter disk 1km up means it will cover about 174° of the sky at the center, $atan2(20,1) \times 2$ or just about all of it. Given the average 12 hours of Sun, that means the surface at the center will get just 20 minutes of direct sunlight a day. And at a high angle.
As we move closer to the edge, things only get slightly better. At 10 km from the edge, it covers 172° or $atan2(10,1) + atan2(30,1)$. At 5km it's 167° or about 50 minutes of daylight. 1km from the edge it covers 133° of the sky, 3 hours of daylight. At the very edge, half the sky is still covered giving only 6 hours of daylight. Even forest not directly under will still be partially shaded from the Sun for kilometers around.
Weather Patterns and Rainfall
Having what amounts to a 40km diameter sheet 1km up will play holy heck with the weather patterns and rainfall. The surface will be cut off from medium and high level clouds, and 1km will cut across many low level rain clouds which tend to be vertical. The ship itself, acting as a sheet, will tend to hold in moisture.
I'm not a meteorologist and cannot predict the exact effects, but its going to mess up the weather.
A Whole Lotta Everything's Gonna Die
Obviously this doesn't bode well for the forest under or even near this object. A tropical rain forest consists of four major layers each which get different levels of sunlight. But even the relatively dark forest floor gets some light. And they all rely on the nutrients provided by the upper canopy. With severely reduced sunlight, this carefully balanced ecosystem which relies on a constant supply of sunlight to power it rapidly breaks down.
Temperate forests must undergo seasonal change and regular reductions in sunlight for the winter, so their flora and fauna store a lot of energy for the winter. Tropical rain forests don't have to deal with winter. In their highly competitive environment, all energy is used to compete with each other. With their energy source from sunlight cut off, they'll have little reserves to fall back on. Plants will rapidly wither and die cutting off the food supply to most fauna who will then also starve and die (or migrate if they can).
The result will be rapidly growing dead spot in the forest under the ship that will eventually kill most of the forest over 40km around. Even plants used to growing on the forest floor in low light will not survive without the nutrients and protection provided by the rest of the forest.
Unlike temperate forests, rain forests have poor soil. Most of their energy and nutrients are locked up in their biomass. Anything that dies is rapidly recycled by scavengers. This poor soil means once the forest is gone, little will grow back. The long term result is similar to what happens after we clear cut a rain forest: desertification.
The forest under and near the ship dies and all the animals die or leave. Insect and microbial scavengers will thrive for a time, but eventually run out of things to scavenge for food and die. Evolution cannot account for such a rapid change in the environment.
What will be left is a dark, barren landscape.
The price Wakanda will have to pay is losing over 1250 km2 of rain forest and damaging another 1000 km2. This is larger than many island nations, roughly the size of Luxembourg. While the size of Wakanda is not known, it is not a large nation, and this could represent a very large chunk of their land area.