That is, is CR simple a proxy / correlation for putting less (modern) shit in your body?
No, you can take a drug rapamycin that has the exact same effects as CR, even if you are putting the exact same amount of food in your body. The benefits of CR are not caused because food is damaging, and less food is less damaging. CR is your body noticing it's running low on food and telling your body to do some maintenance. Rapamycin does the exact same thing, causes your body to enter maintenance mode.
And, best I can tell, if it goes in your mouth than it's about your gut (bacteria). Any downstream reactions are communicated via those bacteria.