The living Earth will be fine, and has recovered from worse than us, even other runaway mutations from within that wreaked havoc, see the carboniferous period and the trees that couldn’t yet effectively decompose and release their carbon, doing the opposite of us, creating an ice age.
The Earth recovers, It just won’t recover on a timescale we can perceive.
There’s life that’s evolved to survive in acid pools, at depths we can’t touch, in crevices we can’t reach. We arrogantly fashion ourselves Gods of this world, but we couldn’t sterilize it if we wanted to.
We will be gone, sooner rather than later because of our actions, but the 3.8 billion year old living Earth will be fine with a negligible few million years of cleanup, and to paraphrase George Carlin, it will be like we never even existed at all, thank goodness for that.
"The sword of God, the blood of the lamb, vengeance is mine, millions of dead motherfuckers, all because they gave the wrong answer to the God question. ‘You believe in God?’
‘No.’
BANG Dead.
‘You believe in God?’
‘Yes.’
‘You believe in my God?’
‘No.’
BANG Dead.
‘My God has a bigger dick than your God!’"
-George Carlin