The issue with CO2 is that there's not a lot of it in air. The amount is usually expressed in parts per million. It's a bit over 400 these days. Way up from around 280 where it used to be. Only about 0.04% of air is CO2. Which means that by mass and volume, you need to process enormous amounts of air to get a meaningful amount of CO2. The main issue with that is that it requires enormous amounts of energy and large scale infrastructure that by itself is quite wasteful. Once you have it captured, processing it and up-cycling it is not that hard. It's nice that we have some new ways. But it's not like synthetic fuels and plastics weren't already doable for decades.

Carbon capture of course technically works. But you typically end up dumping the CO2 back in the air for things like fuels and plastics after they are expended. So, it's not that meaningful ultimately. You take fossil carbon, you burn it, you capture it, you create another fuel, and you dump it in the air. Because we simply don't capture the overwhelmingly vast majority of fossil carbon that we process and use. Using the carbon twice is a modest improvement. Three times even better. It's not that much of an improvement. Most carbon capture is stupid like that but it sounds nice if you are trying to green wash your CO2 intensive business. Optics and marketing are the main driver for carbon capture schemes. But technically it's just adding cost to things that are already quite expensive.

Keeping the CO2 captured permanently is a bit hand wavy usually and technically a bit of an afterthought usually. We might do this, we might do that. It's going to be amazing. We could have, and would have, and eventually might do some of it. Or none of it. Or somewhere in between. The real world effectiveness of carbon capture to date is generally piss poor. Some people would say it's a scam. And the real worlds amounts of carbon captured ever are so meaninglessly low that dumping all of it back in atmosphere right now would not have any measurable effects whatsoever relative to the still growing amounts we dump into the atmosphere directly.

Anyway we have great carbon capture machines readily available. All plants and trees do this naturally. Burning that stuff to create CO2 is a bit wasteful and not technically that useful if your goal is to process the carbon further. Wood is basically polymers. Much easier to use that directly. Either as a fuel or as a source of polymers (e.g. cellulose) and other carbo hydrates. Of course farming and forestry are hard work and not that cheap.