Hey fellow Affinity Publisher users. I found this page by doing the same thing. Looking to see if Publisher could print label and it didn't. I to didn't stop there. lol I went to Avery labels and found the templates section and what I did to get the perfect label of a whole sheet or just one single label was to download the PSD template and Like Magic I was able to print my labels as I like. Just remember to turn off the template layer before you print. I hope this helped you just as it did me. I'm new to the whole Affinity Suite, But I am loving every wonderful minute of it. Game Changer!
Plus here is the link to Avery Templates and I also added the template I use for reference if you need it. https://www.avery.ca/downloadable-templates.html
Avery8160AddressLabels.psd
