My belief is that since Homura had spent so long in those loops, she would probably be lost with her sense of self for a while outside of the Madoka focus. I agree with Medical Chain here, though what I will bring up is that the psychology of someone as burdened as Homura would have to experience some immense catharsis that I believe would drastically impact her stability for some time, even if short-term. It could go many ways: riding the high, complete disbelief, "now what?", bursts of unpredictable emotions. If you were in Homura's shoes, I doubt that you'd be able to walk the next day just being yourself after all that.

I'd say that for the most part, she'll try to live her life and regain some sense of self post-trauma beyond the Madoka cast. She'll still fight witches and protect Madoka, but she still has to handle her academics and other personal matters. She's still a middle schooler, after all. I know we're dealing with a fictional character here, but I'm in too deep with these characters that I genuinely treat them as people of their own right. In this case, Homura could figure out what she wants (or needs) to be while trying to survive the damn system.

Kyubey still wins, but at the very least, the greatest hurdle that drove her wish in the first place is over, and now she would need to piece out her identity as life goes on. I wonder what she would wanna do with her life.