What are the destructive impacts humans had on the planet, and how are we shaping this new geologic era?

Geologic era? Those are not political and take a million years, minimum.

We have 0 effect on the planet. The planet just keeps spinning around the sun, and it will do so another few billions of years. We have only locally effect on the surface. A few degrees more heat, some pollution here and there, but 'pollution' is something weird, because all pollution is stuff that is made from stuff coming from the Earth, right? So a few dozen animal species go instinct. The planet does not care, it keeps rotating en orbiting the Sun. The planet isn't even an identity, it is simply a collection of elements packed together in a sphere.

Way too many things to list here. A few are over-population of humans, mass environmental destruction, greenhouse gas emissions, killing off species of animals and plants, etc., etc.

agriculture depletes the land, knocks down rainforests to grow palm oil and feed vegans.
Oil drills - sucking the literal blood from the earth.

Sounds like a Common Core test question.