I think you're spot on in your observation. Reducing methane would help and definitely has its place, but CO₂ is a totally different beast. CO₂ is best thought of as a "stock pollutant" meaning that the more you have of it, the worse the effects. This follows directly from that fact that CO₂ sticks around in the atmosphere for millennia, increasing atmospheric radiative forcing. Methane, on the other hand, is better framed as a "flow pollutant" - it's harm is ~proportional to the rate of emission. This is a direct consequence of its much shorter atmospheric lifetime.
And if you're up for a pretty technical (but still fairly approachable) read, check out R.T. Pierrehumbert ''Short-Lived Climate Pollution.'' Annual Review of Earth and Planetary Sciences 2014 42:1, 341-379 [https://doi.org/10.1146/annurev-earth-060313-054843]. Near the end of the paper, he delivers this gem: "Methane mitigation is like trying to stockpile bananas to eat during retirement. Given the short lifetime of bananas, it makes little sense to begin saving them until your retirement date is quite near."
Here's a useful twitter thread from a real expert: https://twitter.com/hausfath/status/1425572803508465664
And if you're up for a pretty technical (but still fairly approachable) read, check out R.T. Pierrehumbert ''Short-Lived Climate Pollution.'' Annual Review of Earth and Planetary Sciences 2014 42:1, 341-379 [https://doi.org/10.1146/annurev-earth-060313-054843]. Near the end of the paper, he delivers this gem: "Methane mitigation is like trying to stockpile bananas to eat during retirement. Given the short lifetime of bananas, it makes little sense to begin saving them until your retirement date is quite near."