Thanks for the response!

I had no idea the light gray colored sleeve was aluminum. Sure doesn't look like it to the naked eye.

Since I can't tell how deep the sleeve is, I don't want to risk tapping down the star nut because it could potentially go too far and drop loose into the steerer tube. I imagine that once it falls down you can't get it out...

Can I just bend the star nut prongs inwards with some needle nose pliers and pull the star nut out completely? This would be ideal since the new headset comes with a star nut anyhow. I know it doesn't matter, but I want to get this one out since it's starting to rust.