Shipments

^But it must've had it's own water supply in order for it to have an atmosphere

You don't need water to have an atmosphere, just any gas. If it rains there, it would be different. Could still be shipped in, though.

It could be imported from offworld or chemically synthesized. The atmosphere is likely artificially maintained and cleaned somehow; they might even simply import clean air. Whatever the case, keeping Coruscant habitable must be a drain on the galaxy's resources on an absolutely ludicrous scale.

Or, it could be like the 1700-1800's where people mainly drank booze due to the lack of clean water

It is probably imported from other worlds, as even if it rains, the water wouldn’t be enough to supply the entire planet and it would probably not be safe to drink due to all the toxic gasses in the atmosphere.

There are a lot of planets that did not have sentient civilizations and tonnes of clean water they could take as well.