Early morning thought, but I have a feeling Rasputin will not be so pleasant when Ana gets him up and running.
Before Rasputin went offline, he was operating in a mode of survival at all costs. He'll wake up to several missing stations, many of which he had direct links to, the witness looming on the horizon, guardians using dark powers, and aliens living in the city. I think if anyone has a chance to talk him down it'll be Ana and Mithraax, but he will not be happy. I could see him giving the Vanguard and ultimatum, and potentially see him try to take control from them.
Another possibility, honestly the worse one for us, is that he may become a disciple. The Grand Overture lore tab mentions that, in the mindscape, Rasputin is surrounded by thorns. Notably, thorns are shown in Vow of the Disciple, when both of the bosses die. It's assumed that the thorns are some manifestation of darkness. A symbol of the Witness's influence. The Witness is smart, if he let even a fragment of Rasputin survive, it means he has a plan for him. If the Witness "spoke" to Rasputin, especially in a weakened state, it may have swayed Rasputin to change it's directives. Maybe trick Rasputin into attacking the traveler.
One big thing that's always bugged me is the cutscene where Osiris confronts Rasputin. Osiris says he saw something in the Infinite Forest. Something Rasputin did. Though Rasputin inevitably helps Osiris, I've always wondered what he saw that would be so important to confront Rasputin directly, and not raise a flag, even to us.
Just some thoughts
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Very cool ideas