Hi ESP,
Welcome to the forums
Please try the following:
Open the Mac App Store
Log out of the store
Restart your Mac
Log back into the Mac App Store and go to Updates - if the update is still not showing please try using Store>Reload Page from the top menu.
If the app update is still not showing and you're being prompted to purchase the app, is it possible that Affinity Designer was purchased under a different Mac App Store login?