"The problem with the anthropogenic increase of CO2 in the atmosphere is that it is very recent, very significant and very quick."
None of that is factually correct. In the below chart, the present day is on the left. CO2 is as low as it has ever been during the existence of Earth.

You can also see that there is no correlation between CO2 and temperature on a geological scale.
On a more recent scale, you can see that CO2 in the atmosphere does not correlate to atmospheric temperature during historic times.

IMG source - i0.wp.com/www.climate4you.com
So, you can see that CO2 has not precipitously risen, or is anywhere near unprecedented levels, at least insofar as sober science can show. Further, as it is at a geologically low point, the availability of CO2 to photosynthetic plants is dramatically decreased and global fecundity is extremely depressed.

In fact, NASA states that deserts are decreasing in extent and ecosystem productivity has increase ~30% since the industrial revolution began to add CO2 into the atmosphere that natural processes have slowly depleted over many millions of years.
"A quarter to half of Earth’s vegetated lands has shown significant greening over the last 35 years largely due to rising levels of atmospheric carbon dioxide, according to a new study published in the journal Nature Climate Change..."
https://climate.nasa.gov/news/2436/co2-is-making-earth-greenerfor-now/
The fact remains that NASA, the IPCC, and the full panoply of lying institutions continue to promote the AGW propaganda, despite the scientific data showing otherwise.
The data, however, speaks for itself, and disproves the false AGW claims.
I strongly recommend that anyone interested in understanding the actual climate science, and not being bamboozled by the fraudulent studies that are published for the purpose of false propaganda, go to WUWT.com and research the matter for themselves. It doesn't take long to learn how data is falsified, studies cherry pick the data they include, or that not one of the dire predictions made by so-called 'climate scientists' has ever come true.
It is notable that the environmental movement was born out of the Rockefeller oil fortune, through the efforts of their agent Maurice Strong. Big Oil doesn't oppose the climate change industry. They fund it. The AGW environmental movement (anthropogenic global warming) isn't fighting the oil industry. AGW is the weapon of the oil industry.
You might wonder why habitat loss, chemical pollution, endocrine disruption, species extinction, and much more dire environmental harm isn't so strenuously decried and opposed by Big Oil. Those are all things we can actually do something about, after all, and that are all caused by industry, from agriculture to mining/petroleum. They don't talk about those things. They're only interested in CO2, which they want to buy - all of it - with carbon credits.
You'll have to try to understand why the people with all the money in the world want all the carbon, the very basis for life on Earth, to be able to be privately owned via carbon credits, but with consideration of the history of corporate ethics, that's not hard to figure out either.
Edit: You stated:
"No one is denying that solar cycles are the main driver of the Earth's climate..."
But the sun isn't even a factor in the IPCC climate models, so any influence of the sun is, in fact, utterly denied. The entire AGW industry ignores the influence of the sun. Completely.
Thanks for the info. I'll look into that when I have the time. I can see the business logic of owning carbon credits. But losing the hydrocarbon business has got to hurt as the world pivots to nuclear and renewables.
Interestingly, when they have the carbon credits, they have the ability to burn hydrocarbons, which is what happens to hydrocarbons for the most part (other than chemical processing or lubrication). The oil business will be peripheral to the carbon business, but will not end. It won't ever end, regardless of what happens politically, because humanity requires portable energy and there isn't any alternative to it.
I don't agree with the portable energy argument. Electricity is easily portable using power lines or cables. Electric vehicles are taking the world by storm. Batteries are constantly improving. Energy can also be stored as potential energy or heat. Combustion is not really necessary.
As an Alaskan, a former commercial fisherman, and someone that has flown intercontinental distances, I assure you that you absolutely cannot do those things with shore power. Batteries exist,and do improve constantly, but not enough today to do those things reasonably well and profitably. Combustion is absolutely necessary, and as soon as your life depends on one of those things, or another that require it, you will gain understanding you lack, either through combustion saving your life, or by dying for the lack of it.
And what percentage do those use cases represent of today's total?
Let me whip out a napkin and parse the propaganda to extract the actual real data...
When you are on a fishing boat at sea, 100% of your power comes from combustion. For riding a Segue in the city batteries are fine. There isn't enough lithium in the world to make the billions of car batteries a complete change over to EV's requires. Therefore promoting the complete cessation of infernal combustion isn't promoting EV's, but people without private transportation at all.
What prospect does civilization have that is leashed to it's overlords of being free and prosperous?
None.
Free people will always require, and have, combustion to power their enterprise. Fire is perhaps the fundamental technology that separated humans from other animals, and eliminating human control and possession of fire eliminates humanity, and replaces our human rights with slavery and chattelization.
My question was what the percentage of the total out of all combustion was that cannot be replaced.