Reason being it’s not included is that you SHOULD NOT be using the AUR without knowing about it or why or how it works.
Here’s what Arch says about it:
https://wiki.archlinux.org/title/Arch_User_Repository
That being said, the AUR isn’t supported directly by Arch, and therefore, I could not recommend trying to support it here either. If someone is asking about clearing it’s cache, then they are already in over their head.
Admittedly, we as a distro do include and ship yay in a base install. If I had it my way, and in my very humble opinion, yay would NOT be included in the normal installation process. I think anyone who wants to use it, should know how to build at least one package properly prior to using the entirety of the AUR. But so far, my opinion about leaving it out has not been agreed upon.
tl:dr - AUR isn’t supported by Arch, and neither will we (or at least me in my guide)
Edit: actually, they may even be over looked by pacman. I can’t remember now that I’m thinking about it. AUR packages may be managed by pacman -Sc. Maybe someone else can chime in. It’s been some time since I’ve tried this.