Yes. the atmosphere traps heat.
Great, we have taken the first baby step!
I'm not sure about "equilibrium" here. Is that an assumption or an observation?
It's an observation that is well explained by physics. A fact, if you will.
Does it have to be one equilibrium or can Earth slide from one equilibrium (say, heating the ocean) to another (storing energy as biomass)?
Yes, the equilibrium can change, if one of the factors contributing to the energy budget changes, that's the whole point: that may be i.e. the amount of energy coming in (variations in the sun) or the atmosphere's ability to trap heat (yep, this one is what it's all about: more Co2 increases that).
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