For the most part, I agree that Sirius living could have changed a lot for Harry, except as far as the connection with someone who knew his parents is concerned. He was able to write to Sirius, and talk to him a good bit that summer before fifth year, so he was already able to learn about them. And after Sirius's death, he had Remus, who knew his parents as well. The difference for Harry feeling he has a family and for the battle would be there, but I think any change it would make for Harry learning more about his parents is pretty negligible.
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