If you bought them from the Affinity Store there is no need to sign in to your account unless you want to retrieve your product keys. You can download the latest versions via the Updates pages.
https://store.serif.com/update/macos/designer/1 https://store.serif.com/update/windows/designer/1
https://store.serif.com/update/macos/photo/1 https://store.serif.com/update/windows/photo/1
https://store.serif.com/update/macos/publisher/1 https://store.serif.com/update/windows/publisher/1
