Much of their people and way of life actually survived the fall of the League. However being restricted primarily to living in the water it took some time for them to rebuild their surface holdings. It was also dangerous for many years to walk on the surface as nuclear weapons had been used against them. Even so they eventually rebuilt to walk the surface again in their protective suits and nurture new life in the land.
They also returned to space, but due to their nature they had little interest in actually colonizing or developing the other worlds in their system. Prefering instead to build up their defenses of their homeworld hoping to avoid the fate they suffered during the civil war era from ever happening again. They happen to be near the modern day border of the Galactic Commonwealth and may eventually join it. For now though a limited number of them act as merchants and agents gathering information about the galaxy while the rest tend to stay home and continue developing their defenses.
The Federation of the Quari is unique in that it is run by a monarch, while the ‘nations’ making up the federation can vary in their own governmental types. This means they are the only known federation lead by a Queen. Many of the respective states within their federation or pact are republics with elected officials who report to the queen.
The Quari have a formal military and because of their aquatic nature have custom equipment and vehicles. All of their designs capable of landing on a planet are also capable of functioning underwater, which is a unique feature of their vehicles. Unlike many smaller governments they have their own cruiser design and a batch of cruisers in their current arsenal. However this is at the cost of corvettes and Frigates. This has caused them to use fighters for basic tasks like planetary patrols.