Learn Hardcore Korean: chimsil jomyeongi kkeojyeo isseoyo.

It marks a resultant state. With intransitive/passive verbs like 꺼지다/켜지다, V-아/어 있다 means the subject is in that state as a result of a prior action. So 꺼져 있어요 means it is currently off and remains off.

How is 꺼져 있어요 different from 꺼졌어요?

꺼졌어요: a completed event (it went off/was turned off).
꺼져 있어요: the present state (it is off now). Also, 껐어요 (from 끄다) says someone actively turned it off; 꺼졌어요 doesn’t specify who.

Why is the subject marker -이 used on 조명? Could I use -은 instead?

조명 + 이 marks the grammatical subject of the descriptive predicate 꺼져 있다. 은/는 topicalizes: 침실 조명은 꺼져 있어요 adds contrast (the bedroom light is off, but others might not be). Both are correct; choose based on nuance.

Why not say 침실 조명을 꺼져 있어요?

Because 꺼져 있다 is intransitive/descriptive and cannot take an object. Use:

State: 침실 조명이 꺼져 있어요.
Action you did: 침실 조명을 껐어요. (from 끄다)

Can I use 불, 등, or 전구 instead of 조명? Which is most natural?