It's true that CO2 follows temperature. With the warming from the Little Ice Age there would have been a 5 to 10 ppm increase in CO2. Instead there's about 2.5 ppm per year with a total of 134 ppm so the bulk of that increase can't be from warming oceans. Instead the bulk is manmade from fossil, cement production, deforestation.
The seasonal cycle is partly the seasonal temperate like you said, but also the plant uptake and release. Notice that CO2 rises in winter and peaks in spring when plant uptake kicks in. The average temperature of the planet peaks in July because of the much greater land mass of the northern hemisphere. Land warms quickly each year. If CO2 responded mainly to temperature it would not start increasing at the beginning of the winter and not start decreasing before July.
The "settled science" that CO2 is a "greenhouse gas" that causes "climate change" is therefore criminal sophistry.
CO2 is clearly a greenhouse gas because it absorbs and releases particular bands of IR. O2 and N2 don't absorb and release nearly as much in their bands. The issue is how much each greenhouse gas warms as concentration increases. CO2 is logarithmic so less and less warming with increasing concentration. Also the CO2 warming is greatly exceeded by water vapor warming with long term (decades) down to short term (hours) cycles.
The atmosphere contains 0.04% CO2.
Man is responsible for 3.4% of that 0.04%
The total amount of anthropogenic CO2 In the atmosphere is therefore 0.0014%
Completely eliminate man’s contribution and the Earth’s atmosphere still contains 0.04% CO2.