Methane breaks down into CO2 and water in a few years, which is why half life of methane is relevant. My understanding is that for CO2, thinking in terms of half-life is less relevant, the CO2 goes to plants and to the ocean, and if those two sinks are at saturation, then CO2 levels in the atmosphere will keep increasing.

But there's a good article I found now which might shed more light : https://euanmearns.com/the-half-life-of-co2-in-earths-atmosp...