It's a conclusion of sorts, and never explicitly stated in the game, but – at least if we're working with a broader idea of rebirth – pretty much the only explanation there is.
The very first scene of Chapters, switching from April's funeral right into the House of All Worlds, that was ample hint enough. We saw seven year old Saga remember vivid details from April's life, including especially her companionship with Crow that Saga will eventually continue. We've been told again and again that April is reborn, both by Abnaxus and Storytime April herself. And lastly, Lady Alvane at the very least says that she experienced April's story through her own eyes.
Basically, there's either a form of reincarnation at work here or there is an infinitely worse explanation, with no third option at the horizon.
Hey Ubisoft, you can keep your "seamless vast online GTA in space" to yourselves. Signed, one of the greatest Beyond Good & Evil fans alive.