Was wondering if at 3 years old, there would be hope and good chance to turn the behavior around for F2 female Savannah.
There is always hope, but I think your chances of turning this cat into a pet that meets your needs are slim. We have seen miracles here, if you use the search function for "Ziggy" and/or "Chris Elliott" you'll read a story of a terrified, large male SV who turned into a lap cat with A LOT of time and effort. Not all stories have a happy ending. And in Ziggy's case, his attitude was due to his original owners' actions. Once he learned that not all humans were bad, he also learned how to trust. Chris was a special person with the patience and compassion necessary to work a miracle.
If the cat you're contemplating prefers animals over humans because she wasn't properly socialized or experienced a traumatic or scary event that turned her off, she may turn around given enough time and patience. If she is simply the type of cat who doesn't think humans are worth her time, then nothing you do will change that. If there isn't another pet in the household that she can take comfort in, it's anybody's guess how she would redirect her need for companionship. And even if there is another cat or dog in the house, you'd have to engage in the process of a proper introduction to that pet as well as attempting to overcome the challenge of a cat who doesn't necessarily tolerate human companionship.
I have an F2 male who is 7 yrs old and he prefers the other cats over us. It took 3 yrs of working with him at his pace to get him to tolerate being touched. I still can't pick him up and he won't sit in my lap but he shows his acceptance in other ways. He sleeps with us, engages in play, gives love eyes, and allows limited petting on his terms. Bottom line with him though is that he'd be perfectly content if we weren't around.
If this is your first Savannah, I recommend waiting for a cat that is more suitable for your household and needs. SVs are challenging to own when they don't have issues and she is a high gen SV which we would hesitate to recommend to first-time owners even as a kitten.