Calibri works just fine on my machine. Just download the font using one of the many font packages available in your distro (i.e. https://aur.archlinux.org/packages/ttf-ms-win11)

I don't think it's included by default but the font itself will just work once you install it.

As for open fonts (can fonts even be truly closed in the first place?), Times New Roman is just as closed and proprietary as Calibri is.