"I think Fermi's Paradox is more interesting than Drake's equation. "Where the hell are they?", that's the puzzler."

What would these advanced civilizations want?

We have been living in last 100 years or so with various myths.
A common one is that we will continue to have a population explosion. That's pretty well de-bunked at this point, but still people suffer from such delusions.
And the resource depletion is also myth which has long been de-bunked. Though energy resources are still something serious people have some justification in worrying about. To be clear, this of course has to do with the shortage of cheap energy, as compared to all energy resources.
But regardless of whether there is actually at this point in time shortage of cheap energy, it's quite possible that our future could be such that we have nearly infinite amounts of cheap energy [cheaper by factors 10 or 100 as compared to today]. Or even without this factor, the cheapness of energy could at some point could not be important. Today the amount energy used by a nation is direct relation to the country's wealth. In the future it could be utterly unrelated to it.

So it's possible that Human population never gets as high as 10 billion or 20 billion- this could be true even if we have colonize every planet in this solar system and it's thousands of years from now. And the solar system could theoretically support a 100 trillion of humans. And if think this is because humans have got smarter or because of Chinese birth control program- you missing the entire point. It was never about getting smarter or having a government program. You might in the future have government program that encourages people to have more children- and it's possible it won't work. I mean, if you want something like The Brave New World, obviously that works but people might simply have no political interest in factory produced humans.

Anyways, say we living in a solar system with 20 billion [or a trillion or 100 trillion people] we have unlimited supply of cheap energy and no shortage of any resource.

Suppose you had warp drive technology and can travel at light speed. If you travel at these speeds, you are cutting your self from your society which isn't traveling at near light speed.
You leaving behind your life. You doing something similar to killing yourself [to go on a "trip"]. You are time traveling into the future. What is the need of doing this? And if you choose to time travel, why not have as your destination "your world" in the future [leave and come back]?