I am not sure if we are not mixing up things together.
I thought that you meant using apple script as scripting language for Affinity products (it's not only about publisher). Meaning scripts that Affinity can run to control itself (and get low level control) like transforming text, populating frames with images, get data from excell table, connecting to web to grab something, drawing points and lines... basically anything. For this AppleScript would be a bad choice because its old (last version 2014) and does not have any ecosystem (dont forget the amount of libraries javascript or python already have for any possible usecase) and it's not open-source.
It seems that you talk about ability of Affinity programs to be programmable/automatable from outside with applescript or things like automator. This is very different thing. But this type of programmable user actions is on OS level and you can already do it.
If you put this in OSX Script Editor
tell application "Affinity Publisher Beta"
activate
open "/Users/user/Documents/test.afpub"
end tell
It will work and you can script user actions in the software.
I guess adobe is exposing more controls to OS so more things can be automated this way (and they have it documented here https://www.adobe.com/content/dam/acom/en/devnet/photoshop/scripting/Photoshop-CS6-AppleScript-Ref.pdf ) so you might want to want for Affinity to think about this. Who knows maybe it is easy for them to expose more functionality this way. There is probably some work needed to be done so script editor get documentation like some other software (screenshot of Adobe Illustrator) currently it doesnt.
By the way Apple it seems is already moving away from Applescript to Javascript for OS level automation. In script editor you can switch to Javascript mode and do everything. They cal it JXA - javascript automaton. https://apple-dev.groups.io/g/jxa/wiki/JXA-Resources
But overall i think people in this thread are mainly interested fairly low level scripting access to Affinity products.
Personally i never found much that much usecase for automation of GUI apps on OS level. On the other hand what i totally need for my work is to generate PDFs. Imagine for example you are making book of all pantone colors from excel table - this would be insane without automation (and yes you can generate those pdfs somewhere else but ability to still edit afterwards is priceless).