“expand the lines” in Inkscape is Path->stroke to path.
Basically, make your circle, then set the line width to however thick you wanted the engraved area to be. Then go to Path->stroke to path, it’ll turn your circle into a “donut”, meaning a filled ring, waiting to be engraved.
This is similar to what you would have done with the text when you did “object to path” to convert the letters to filled shapes.