I am so sorry about your girl!

You have been given some wonderful advice here so I will just add my 2 cents here!
From past experience with birds and heart conditions, I doubt this is a heart issue. The reason being is that generally when the heart leaks fluid out into the heart chamber and into the body cavities, had it leaked this much fluid into the belly, the heart would have stopped by now. It would have over whelmed itself with fluid and stopped beating. It only takes a small bit of fluid in one of the heart chambers for the valves to clack loudly and with no room for the valves to function, the bird goes into cardiac arrest and dies of full blown heart failure. Draining the belly would thus drain the heart valves and the bird would then be able to breathe, however with heart failure, the belly continues to fill. Birds use the muscles in the abdomen to breathe. And the size and fluid amount in your birds belly would have strained the heart enough to stop it long ago.
A gizzard blockage wouldn't cause ascites although a distended liver could block the gizzard from emptying and liver disease can leak fluid into the belly. BUT...liver bile is green, and your fluid looks more clear, so I don't believe she is suffering from liver issues either.
Its hard for me to see the exact color of the fluid, however if its clear to pale yolk yellow, most likely she is internally laying. Hence, green liquid can mean liver, deeper yellow straw color is body fluid and can mean heart failure and clear to yolk color yellow can mean internal laying. (These colors are a guide line and not always written in stone).
Dark green poop can stem from a lot of issues and no doubt she has several going on right now from cocci infections, E.coli, yeast and possibly Enteritis. Cancer will also cause deep green poop.
My thoughts on her is that she is mainly suffering from either internal laying or has some sort of reproductive cancer with several other secondary infections going on at the same time.
There isnt any real hard core cures for either of these, sometimes a couple rounds of antibiotics will extend their lives but generally they don't survive these diseases. Definitely don't drain too much too fast, poking 5 or 6 holes, sucking out 2 mls at a time and letting her drip dry on doggie pee pads is the prefered method. It takes 24 or so hours to drip themselves dry. You can also try either PenG injections or Amoxicillin orally, either of these for 7 days and along with a draining, she will definitely be more comfortable.
Good luck with her!! I know how difficult this seems!!
