Affinity Publisher uses the Hunspell Engine for spell checking and it also allows for additional Hunspell dictionaries to be added. You can download additional dictionaries from LibreOffice's GitHub page here but you can find direct links in the below post.
Once you've downloaded the correct file(s), you can use them in Affinity Publisher by following the below instructions:
Please note: There are some differences between how you install Hunspell dictionaries for macOS/Windows,