Just to back up what your saying MIT have a nice explainer on carbon lifetimes[0].
I don't know if I feel as doomed as you though. There is a lot of technology to reduce carbon (renewables etc). And moreover, a lot of the carbon use today is completely unecessary consumerism.
We've had 30 years of political inertia since Regan/Thatcher/etc so political change seems impossible to a lot of folks. Historically that's just not the case. Before then, voter rights, civil rights, women's rights all made huge political changes. If there's any silver lining to the horror show of US politics at the moment, it should be that there is at least proof that massive structural change is possible in today's political climate, and I genuinely believe that can be harnessed for good.
I don't think there's any guarantees, but it's still a lot too early to give up.
[0] https://climate.mit.edu/ask-mit/how-do-we-know-how-long-carbon-dioxide-remains-atmosphere