The end
I just now understood, that I didnāt post anything here as an update.
So, in short, AsusRouter is not expected to be added to Core anymore, since this will cause confusion to users if having 2 integrations and having only AsusRotuer will cause issues to users of 15+ y.o. devices which did not support API yet.
In any case, the core AsusWRT added HTTP(S) API support a bit more than a month ago (link).
So, maybe at some point, it will start working properly for the users
AsusRouter will still be available as a custom integration for all those voting for a feature-full experience
You can also use the backend library for your projects
Meanwhile, this feature request is one of the largest (top-36) in this community forum