I tell my clients that when we do a line edit, I can perform about 90% of the tasks that a true copy editor can, because I am an expert when it comes to grammar and punctuation.

And that running their work through Grammarly will pick up those few errors that I've missed.

That being said, I would not hold myself out as being a copy editor. That is, as you say, a specialized form of editing.

Thanks for asking!