The left half with the straight vectors seems to be just fine, although when I tried to import the PDF, it only imported the cut lines of the tangram and didn’t include anything of the graphic.
The right side with the graphic with the text has several issues that need to be addressed. The files has clipping paths which can be an artifact of using PDFs that I tried hard to get rid of but couldn’t. In the end they made no difference. Then there was the white circles under the text to block out the underlying graphic. That won’t process the way you want it to. You have to directly clear space in a graphics program. You can’t just put a white colored layer over the engrave you want to cover. When I imported the PDF into Inkscape and then exported that as an SVG to bring into the Glowforge UI, it brought in several copies of the saying/text and then noted about the clipping paths.
One way is to keep the engraving/graphic as a separate graphic and save it as a PNG or whatever. that keeps your options open. When you process the cut file, you can import the graphic or whatever graphic you want to put in after you open the cut file. It also isn’t the best resolution so you aren’t going to get the crispest engraving. It’s grey and not a whole lot of dark, but I’ll see how it works.
Put the text that you’ve converted into vector for engraving in one color. Put the outer cut into another color and separate from the other cut which will make the pieces and the border/ring to contain the pieces.
Here is the file as I would use it, cleaned up in Inkscape and saved as an SVG. Maybe you can look at this file and get a sense how to put them together. I tried to embed the graphic in the SVG but isn’t showing up in the post graphic. That’s why I keep bitmaps separate and import them as needed. I hope this helps.