I'm not familiar with chainsaw oils specifically, but there's a similar trend in gun lubricants, where many (non-military) ones are vegetabe oil blends with additives that are supposed to prevent gumming etc; I suspect these are very similar, if not the same compounds.
There is still an ongoing debate on whether these are good enough etc. On one hand, some people swear by them, and non-toxicity is especially nice when it's going to be heated rapidly right next to your face. On the other hand, there are certainly quite a few recorded cases of things gummied up when stored long term. It appears that the additives do help quite a bit, but it's still a failure mode to consider, unlike synthetic oils.
Tbh I wouldn't worry much about toxicity compared to the shit in GSR. Anecdotally I've never tried it but some people have tried something vegetable and it went sticky anyway. Cleaning guns regularly is enough of a pain in the ass already without maybe having to before going out shooting. I'd also never use it in a CCW or something ready for home defense because of that risk.
FireClean was notorious for trying to shut up a guy who disclosed that it's basically just canola oil with additives. But even so, there are many people who use it without it gumming up. When it happens, it's usually when you store a gun lubricated without using it for a long time.
There is still an ongoing debate on whether these are good enough etc. On one hand, some people swear by them, and non-toxicity is especially nice when it's going to be heated rapidly right next to your face. On the other hand, there are certainly quite a few recorded cases of things gummied up when stored long term. It appears that the additives do help quite a bit, but it's still a failure mode to consider, unlike synthetic oils.