I'm intentionally leaving the 'way back when' part of the history vague largely for the same reason we don't mention Earth: It doesn't really contribute to the setting.
That aside, these were not the best of colonists, nor did they have the most resources. Those that could leave likely did, and a combination of poor management, bad luck, and limited resources slowly caused the colonies to fail. They build up, fall apart, and build up all over again as they slowly try and tame the planet.
They didn't get rescued, because no one really cares what happens to a bunch of stubborn/poor colonists.
They didn't get out a request for help because all their stuff got broke, yamatai was in a full-scale war, / the plauge / what have you.
And they didn't leave because those that could leave already did. Those that stayed either didn't have a ship or were too stubborn to move on.
It has been so long since the work to terraform this planet has started that the natives now genuinely consider it their home and they'd rather not leave.
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1.5 billion also seems fairly reasonable. Earth has 7 billion and some change. Though live is hard on this planet, there is plenty of space and plenty of food and the colonists have had plenty of time to have lots of kids.
The idea is that the colonists arrived at the planet hundreds of years ago and the how and why they got there is not really a concern to anyone anymore. In that time they've had a lot of babies.
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Algaeia is going to be the reason why the planet has slowly been getting better. It is a genetically engineered algae designed to terraform the planet. Of course, no one is really around to monitor the stuff anymore so it just kinda does its own thing.
Consider it the Neko of small green algae.