~30% natural rubber with the rest being synthetic polymers, woven fabrics, steel, stabilizers, and carbon black, silicates are also included to change the properties of the tire.
If you don't account for the structural components and just tread composition it's probably closer to 40%
Bunch of it is in my lungs too I assume from my days driving trucks, you could see the black rubber dust getting kicked up off the pavement at truck stops when it hadn't rained in a week. Not surprising to me that rubber dust is a particularly prevalent and pervasive pollutant. Also as someone who go karts often you get absolutely covered in it.
This is one of the biggest bummers about trying to be a responsible car enthusiast and track driver to me, there's no real good way around it, and I'm a worse offender than most chewing through sets of soft performance tires.
The only good solution is fewer road vehicles because nothing will replace rubber and plastics for tires, though maybe the compounds can be made less damaging in general that's not going to really solve the issue and it will be made worse with heavy electric vehicles.
The methane just breaks down into an equivalent amount of CO2 when vented anyways and until then is a much more potent greenhouse gas. That's why it's usually flared off apart from safety.