Affinity Designer can be hit or miss at opening PDF files saved by Illustrator. It all depends on what kinds of effects were baked into the artwork. The current version (2.6.3) of Affinity Designer does a better job at it than the version 1 builds. It still doesn't cover everything though.
Illustrator does default to saving .AI files with PDF data included, but that can be easily unchecked in Preferences to save on file sizes. If an .AI file doesn't have PDF data included Affinity Designer will just import a blank document.
Another problem: variable fonts. If the .AI file has any live text objects using variable fonts they'll cause a missing fonts dialog box to be displayed when importing the PDF data into Affinity Designer, even if those variable fonts are installed in the computer. Variable fonts still aren't supported in PDF files. The user at least has the opportunity to import the text as live objects rather than converted to outlines. But the correct numerical variable instances have to be re-applied to the text objects after the file is opened. The missing fonts dialog box only displays text-based styles in a drop down menu rather than numerical sliders. I suppose they could fix that with an update.
I'd rather import a PDF that was generated by Adobe Illustrator than PDF files exported by other applications (including Adobe InDesign). PDF files can be a really horrible mess when imported. Thank God for the Vector First Aid plugin. Illustrator-generated PDF files tend to be much more edit-friendly. If an Illustrator file has artwork properly organized across different named layers Affinity Designer will preserve the layer structure when importing the PDF data in the Illustrator file.