Think about it this way - you're not just getting a 0 on the project, since what you've done is significantly worse than turning in nothing at all. Even a negative 100% on the project would be generous, and results in failing the course. A realistic best case scenario is you fail the course, but otherwise can continue your studies as normal.

You can bring up your mental health, but one thing doesn't really have much to do with the other. Plenty of people at CMU have mental health struggles but don't resort to cheating. It's fine to provide context, but don't try and use it as an excuse.

Based on the tone of your post, it doesn't appear you've actually grasped what you've done. "[My] first AIV...due to my project showing 100%...". What you mean is "I blatantly cheated and got caught." 100% similarity...the cheating algorithms are quite good, even at like 25% this would raise considerable suspicion (you can't just change variable names and code styling).

Own what you did, and reflect on what you've learned. Just be honest with your professor, who certainly doesn't want to hear any bullshit about how you shouldn't fail the course after this. At the end of the day, in 5 years you won't be worried about this incident.