This is easy. It stops because Ana was still deciding to let Red sacrifice himself. Giving us the chance to make the right decision. It was glowing because it was getting ready to reset time and try again. What we did was the right thing and it staying is the proof we are on the right course.

I think it's possible that it stayed bc of Rasputin's sacrifice, but I think if that was the only motive then why didn't it come back down to the city? Unless it went dormant once again and just so happened to be in low Earth orbit at the time. Also did it start leaving bc it knew the witness' fleet was close, or did it do so bc of eramis targeting it? I think either way it knew that something bad is going to happen to it soon, and it moved to prevent the city from being collateral damage. The argument could be made that the traveler doesn't care enough about humanity for either explanation, but I think between Rasputin's sacrifice following the guardian creed and the pyramids closing in made it stay in system but also move far enough away that it can protect the city from collateral damage from the warsats or the witness

At first I thought the Traveler stayed because the Witness said there’s nowhere for the Traveler to run now. But after watching My Name is Byf’s video, it makes sense that the Traveler stayed because of Rasputin performing that line the Speaker said to Ghual in the Ref War campaign.