I’d rather reinstall the damaged file(s)’s owning packages than rsync a bunch of system files. Given this is Ubuntu, I can actually provide advice:
dpkg -S /usr/include/inttypes.h
apt install --reinstall PACKAGENAMEHERE
Messing with files managed by the package manager is a way you damage your system. If you are 100% sure you are not going to damage anything, that’s fine, but be careful when merging a non-prod system onto your prod system. You could do something like damage dynamic kernel module build system (in Debian derivatives and more, DKMS) and break system upgrades.