I wouldn't say "starving yourself", there's no reason to believe it's different from any other diet (except it's easier to stick to). If you get enough calories, prioritize protein, do some resistance training and get proper sleep, you can minimize muscle loss and in some cases even gain muscle while losing fat.
"Ozempic face" is just the result of excessive weight loss. The term is basically putting the blame on the drug for people wanting to continue to lose weight even after achieve a healthy weight.
It's completely unrelated to GLP-1s. 5+ years ago, we would have just called it "Anorexic face".
It has the same effect as starving yourself. Go look up pictures of "ozempic face"