After copying some content and long-pressing on the page, you don't see a Paste option, but instead see Highlight, Strikeout, Define, Copy.
If you're on a custom template, not a built-in one, this is likely related to an incorrectly formatted template. The lines on the template aren't "flattened" and are instead selectable, similarly how you would be able to select text on a PDF document.
If you have a Mac, you can open the PDF in Preview, press command+P, choose "Save as PDF" from the bottom-left dropdown list. Then import the new PDF.
Alternatively, you can open the template in Chrome, click Print > Save, making sure "Save as PDF" is selected in the Destination field. Then re-import that template into GoodNotes.
Another method is to process the file through an online PDF flattening service.