If dental hygiene/healthcare isn't doing it or isn't accessible, then the next best I've found is certain softer wood. I have some sensory issues with anything putting pressure on my gums so I need to constantly keep food remnants out and also have something of an oral fixation so having something in my mouth is calming.

Some tree branches are great for chewing on. I used to live in an area with lots of Sassafras trees and those sapling branches were great for it. They have a bit of a waxy texture that I kind of liked. I've heard they also have a very mild stimulant effect in the bark as well which probably helped when I would grab them when hiking, but they don't have a scent, though you could grab some mint leaves to supplement for that.

I also tend to get some good quality toothpicks (I like bamboo ones personally though they're sometimes not as strong for picking) and soak them in a little bit of good quality tea tree oil that's safe for ingesting (some is only safe for external cosmetic purposes). They're good for picking food remnants which leads to bad breath, as well as chewing and tea tree oil has a mild disinfecting effect as well as leaving breath smelling fresh. But you could also soak them in mint oils (again make sure they are not just cosmetic grade, but also culinary grade).

Those oils are strong, though, so only a little is needed, but might still be too bitter for some. A little artificial sweetener mixed in before soaking might help if the taste is bothersome. Natural sugar is probably not good, though, since it will just make cavities worse and thus make your breath worse.