cuda v13 is in the Unstable & Testing repos:
mbn info cuda -q | grep -Ev 'Name|Repository|Packager'
Branch : archlinux
Version : 13.0.2-1
Build Date : Fri 10 Oct 2025 04:38:56
Branch : unstable
Version : 13.0.2-1
Build Date : Fri 10 Oct 2025 04:38:56
Branch : testing
Version : 13.0.2-1
Build Date : Fri 10 Oct 2025 04:38:56
Branch : stable
Version : 12.9.1-2
Build Date : Fri 01 Aug 2025 15:19:27
mbn can be found in the manjaro-check-repos package
To switch to Testing branch:
sudo pacman-mirrors --api --set-branch testing
or, to switch to Unstable branch:
sudo pacman-mirrors --api --set-branch unstable
After you changed the branch, rebuild the mirrorlist and update your packages:
sudo pacman-mirrors --continent && sudo pacman -Syu
If you are going to use the AUR, then you should be on at least Testing branch, but preferably Unstable branch, which is closest to Arch.