I have a hard time trying to imagine any civilization needing so much energy as that of, say, 1/2 of a Sun's.

They would be very busy people.
I suppose if they wanted to do a lot traveling to different stars or maybe time traveling, this could need a lot of energy.

But if you think in terms of our use of energy [and I see no reason why we couldn't become far, far more energy efficient]
I would guess that probably the surface area of Mercury at Mercury distance could provide enough solar energy for human population of hundreds of trillions.

I suppose I could plug in some numbers and do more than guess.

"The total primary energy consumption of the human race from 1994 to 2004 is shown in figure 1. This covers the major energy sources such as fossil fuels (petroleum, natural gas, coal), as well as nuclear and hydroelectric. The contributions from geothermal, solar, wind and wood/waste (GSWW) are grouped together in the calculations."
http://www.helpsavetheclimate.com/energy.html

So, in 2004 it shows about 1.3 10^14 kWh annually.

So, let's assume 2.0 10^14 kWh annually for 5 billion people. So, 4.0 10^18 kWh annually per 100 trillion people.

Now, a sq meter at Mercury distance and getting 50% efficiency is 9350 kw divided by 2 is 4675 kwh times a year [8760 hrs], so about 40 million kWh.
And sq km is 40 million million kWh or 4.0 10^13 kwh
And 1000 km square is 4.0 10^19 kwh.

So need you need a million sq kms of solar panels at 50% efficiency at Mercury distance per 100 trillion population and this population would use more than 10 times the energy that we currently use.

So, the surface area the size of Mercury could provide enough energy for more than 1000 trillion population.

Frankly a population of 100 trillion people is little beyond my imagination. I think a solar system with more than 100 trillion is a bit over populated and I think if population reaches 1000 trillion, one should seriously consider going to other solar systems.

Can you imagine a human population of 1000 trillion in this solar system? Planet Earth would probably have about a trillion people living on it.