So while it is a tax that benefits the poor, the poor are also paying a higher portion of their income to support it while the Jeff Bezoses of the world remain largely unaffected, can use this disparity to further widen the wealth gap and—for any carbon tax rate that the poorest half of the population could at all afford—continue eating their beef and heating their houses for an infinitesimally small portion of their income.

Meanwhile, the Jeff Bezoses of the world probably have the best means available to lower their carbon emissions. Their wealth could be used to provide public transportation and green energy developments, so I believe that there are more efficient ways to reduce carbon emissions than consumption proportional carbon taxation. Progressively factor income and profit into it instead, and lower other income and profit based taxes to simultaneously reward successful businesses/people with small carbon footprints and make those that benefit the most from poor people driving to and from work pay for it.

Jeff Bezos consumes and releases way more carbon than the average person. Private jets, multiple mansions, a fleet or cars, a private rocket company. He would pay way more into a VAT and carbon tax than a median American. If the UBI is large enough to notice, Jeff Bezos would definitely be affected by the means to fund it.

Meanwhile a person living near the poverty line would get more back than they had to pay in increased prices. On top of the net transfer, they now have a guaranteed safety net without means testing, application procedures, and waiting times that they would still get even if they have to quit a job due to a crappy boss. They can also move cities/states without the fear of loosing their benefits.

Yes, but again, I don't think his carbon footprint has increased proportionally with respect to his income, which if it holds true generally means that a carbon tax in proportion to consumption is regressive in terms of proportionality to income, in which case the poor would be disproportionately affected.

I don't know why you consider it a red herring. Possibly because you haven't understood the argument for why it can be considered a regressive tax (you certainly haven't acknowledged it), but in any other case, instead consider those only a little richer. For example, I can afford living in a large city, near essential services. I can afford living near my workplace. This means I can afford not having a car at all, and if I wanted to, I could afford an electric car. I can afford conscious consumption. In that sense I have better means to minimize my carbon footprint than someone that lives in a rural community, works several tens of miles away in the city because they can't afford to live near opportunities of employment, can't afford an electric car, can't afford to buy locally produced food etc.

The poor may be getting more back than Jeff Bezos (thank god) but the middle class will clearly be the immediately obvious winners in a scheme like this, funded disproportionately by the poor.

So if the poor get back more than they put in, how can they be disproportionately be funding it?

A carbon tax+UBi is not regressive, if the rich pay in more than they get out and the poor get back more than they put in. That is the red herring.

The break even point should occur somewhere in the upper middle class. If it was just a tax by it self you would be right. But the effective tax discount through the UBI makes it progressive.