You are correct, the app doesn't have high res exporting (yet). For the time being you would have to export the shape as SVG and use some other tool to get the high-res image from SVG.
I asked your question to the wonderful Product Manager of Adobe Capture and here is her reply.
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They need to either export as SVG and open that in AI/PS, or drag the shape in from Libraries, where it will also be an SVG and can be sized up or down as needed.
The first option would be:
1. From the shape’s page: choose the left most icon for “Export”, and select SVG.
2. Save this to your iCloud drive on iOS, Google Drive on Android, or on your device, and transfer that file to your computer.
3. On your desktop, in Photoshop or Illustrator, open the SVG.
4. The SVG can be smoothly sized up or down while maintaining detail.
5. Add as a layer to existing artwork Or resize the canvas and artwork to your needs and print from the file directly.
The second option:
1. Open your artwork in Photoshop or Illustrator.
2. Open the Libraries panel, select your shape, and drag it into the artwork.
3. The shape will come in as a linked vector file and can be smoothly resized up or down without losing detail.