How to install warp-cli on Manjaro?

That doesnt have anything to do with the package.

Seems like something is wrong with pamac.

Its probably one of the previously reported problems. Possibly fixed with

pamac upgrade --aur --force-refresh --dry-run

I wouldnt know, dont use it.

Heres the standard way of building an AUR package (including prereqs);

sudo pacman -Syu git base-devel
git clone https://aur.archlinux.org/cloudflare-warp-bin.git
cd cloudflare-warp-bin
makepkg -sric