Tear gas is banned for military use not because it’s exceptionally harmful, but because all chemical weapons are banned. The exception being tear gas use for riot control. One could argue that seeing some kind of chemical weapon used (like tear gas) could lead the other side to use ones that kill in minutes (novichok, sarin) since it’s kinda hard to determine what’s comming “your way” in that situation.
Yeah, no. I said proof. Not “my magical book says so”.