But if the Sun always existed than it will also always exist, right? But then why did LEs eyes going all 8ball indicate that that power source was cut off? Was it because he was also in the furthest ring?

The Cracks in Paradox Space stabilize the flow of reality in the Furthest Ring. The Green Sun has always been there, but much like how there was an event that Created it, there’s also an event that Destroys it. And given the state of everything leading up to the opening of the Breach, there’s nothing ‘after’ the Great Undoing, because Space and Time aren’t weird anymore- There’s no way to go back to the point before the Collapse, and the Rapture is still taking place. It’s truly The End.