I'm pretty sure I read about a treaty or convention from the early modern period that outlawed soldiers from digging shot bullets out of the dead or the ground and reusing them in battle since the bullets would spread infections and normally kill anyone it hit, regardless of the initial bullet wound, but I have no clue what it was.
You might be misremembering things. International treaties governing warfare didn't really become a thing until the 1800s. You may be confusing the section of the 1899 Hague Convention, which banned the use of expanding ammunition (think hollow point or soft point bullets) in warfare.
It's very unlikely that there was something like you described. Getting beyond the historical understanding of infection (something I'm not really well versed in), there's the practicality of reusing spent ammunition. Cartridge cases can be reloaded under some circumstances, but jacketed bullets cannot practically be reused after being fired due to the deformation from the rifling and impact. Unjacketed bullets (solid lead, think 1870s and earlier) would be more susceptible to deformation on impact, but would be easier to reuse, as the bullet could just be melted down and recast into the correct shape. The problem there is the casting process is going to kill any infectious diseases on the lead.