Without controlling for income, it's hard to draw good conclusions here. Looking at the area I am familiar with (Boston and its inner suburbs), CO2 emissions seem to correlate pretty well with income for areas which are a similar distance from downtown Boston and similarly dense/built-up.

Of course there's the open question of whether something like Brookline or even more so Cambridge or Somerville count as "suburbs outside a city".

Also from the area, I get the sense that the Boston area is generally increasing in carbon efficiency (at least pre covid). There simply isn't space to build more/bigger highways into Boston, the only feasible way to expand capacity is increasing density and more transit/biking.