CO2 rise occurs after global warming as warmer oceans release the dissolved gases into the atmosphere.
That's true, and that happens. But the amount does not add up. The entire, mostly natural warming for the last 100 years was about 1C. That would release enough CO2 from the oceans to raise the concentration about 5 to 10 ppm. Instead we get 20-25 pm every decade, way more than expected. As I just pointed out another possibility is natural releases from the earth's crust and mantle, but that requires the explanation of why now and not in the last 20k years of very good records (ice core, stomata, and sediments). A third possibility is the biosphere releasing more CO2 which is definitely true and part of the rise associated with "fossil fuel burning" even though it is not. But it does not account for the majority of the observed rise.