It is not impossible to run yay or makepkg with calamares, to be true easy to do so but from perspective of stability not a good idea.
We have shellprocess and contextualprocess modules.
Both can run inside or outside the chroot and have variables to set chroot path and created username:
@@ROOT@@ // @@USER@@
So while chroot is running as root… you could run yay as created target user inside the chroot…
cd /home/@@USER@@
su @@USER@@
yay -S --noconfirm awesome-dangerous-aur-build
or build package with yay on liveuser and copy it into target, where you can install it with pacman -U
But if one step is failing it will abort installation… and it is a much better idea to do such stuff after the first boot into the installed system.