I am not aware of an additional material on the Laputian civilization from Studio Ghibli but Laputa as a civilization is lifted straight out of Gulliver's Travels by Jonathan Swift (https://en.wikipedia.org/wiki/Laputa). It is unclear how much the Laputa in Castle in the Sky before its civilization fell apart is meant to match how it is depicted in Gulliver's Travels.
Instead let us look at how Miyzaki depicts ancient civilizations.
Miyzakai is fond of using long gone advanced civilizations in his plots. Nausicaa and Future Boy Conan explores many of the same themes. In all three stories, the now gone civilization is almost always depicted as extremely technologically advanced with a complete disregard and disconnect from nature. Miyzaki was a communist in his youth, and his works almost always portray these long lost civilizations as capitalist and greedy. In this context, there are many hints in the movie itself that clue us into what Laputa was like:
- Laputa was an absolute monarchy led by the royal family who controlled the power of the city through their use of their crystals which only responded to their commands.
- Robots were used for both labor and as weapons of war, and directly obey commands from members of the royal family.
- Laputa is filled with gold and treasure of all sorts, implying the Laputians were materialistic.
- The existence of the excellent architecture, gardens, art, and multitude of treasure all show that Laputians thought of themselves as "upper class" compared to the people on the ground.
- Laputa was hidden in a hurricane, showing the Laputians had the power to control the weather.
- Muska says the powerful weapons Laputa has once made it a major world power.
- Laputa's power derives from a special crystal that can only be mined in the ground.
- Very old mines appear throughout Pazu's village and it is stated that the same crystals that power Laputa were once mined there.
- Craters are visible across the landscape in many of the flying sequences of the film, especially seen around Pazu's villiage. Perhaps these craters arose from bombardment by Laputa's weapons.
All of this implies Laputa was an aggressive domineering "hydraulic empire" towards people on the ground that sought to control the mining and supply of crystals that was the source of their power. Real life civilizations throughout history rely on controlling natural resources to be the source of their power and wealth. In ancient times this happened through the control of the water supply, and nowadays it happens through the control of oil.