The true timeline for the twins' story after the 6.5 lore
This is the most accurate take on the timeline of events (so far). I haven't seen anyone in the community post this specific timeline yet, so I decided to share the one I've put together.
Okay, starting at the beginning: the Abyss Sibling actually left the ship right after the twins first arrived in Teyvat. After that, the ship just kept moving without them, with only the Traveler on board.
Then, Asmoday caught the Abyss Sibling and locked them up in the Temple of Space. Later on, the Abyss Sibling managed to escape, but they had to sacrifice their memories to do it. After leaving the temple with no memories, they were suddenly summoned to Khaenri'ah and started living with its people. When they finally regained their memories and went looking for the Traveler, they couldn't find the ship anywhere.
"We'd been separated ever since I awakened in Teyvat. I searched the whole planet, and found no trace of you anywhere..."
(This dialogue is from the story 'Space and Time for You').
But why couldn't they find them? It's because the Traveler was still traveling through space alone, fast asleep inside a stasis capsule, completely unaware that their twin had left the ship a long time ago.
(This is exactly why the Abyss Sibling told the Traveler they couldn't find the ship when they searched for it. It's also the reason the Abyss Sibling wasn't shown coming out of the ship, but was instead seen arriving at it from the outside, because when the ship arrived in Teyvat for the second time, it was carrying only the Traveler.)
500 years ago, the Traveler's ship returned and landed in Nod-Krai, and the events of "Space and Time for You" happened: Direidyth took the ship's key from the Abyss Sibling and gave it to their past self. This was the definitive proof the past Abyss Sibling needed to know the Traveler was actually here in Teyvat.
Once they realized this, the Abyss Sibling left Khaenri'ah and went to the ship to wake the Traveler up so they could escape Teyvat together. But right before they could leave, Asmoday stopped them, trapped them in cubes, and sent them back to Teyvat by order of the Heavenly Principles.
That's when the Abyss Sibling woke up (before the Traveler), and their journey with Dainsleif began. They traveled all across Teyvat until their journey ended at the Sea of Flowers at the End. There, the Abyss Sibling decided to rebuild Khaenri'ah and go to war against the Heavenly Principles. Dainsleif didn't agree with their plan at all, which is why they split up and went their separate ways. A long time later, the Traveler finally woke up, fished out Paimon, and started the journey we are playing right now.
And yaeh, the Heavenly Principles are not the ship's Al, because they already existed before the ship's first arrival.