The impact of a tax is measured as a share of your income - if a tax represents a growing share of your income as you grow richer, it’s called progressive, otherwise it’s regressive (ie falls harder on the poor).

This is the case for consumption taxes in general and carbon taxation in particular. This is not contradictory with the fact that the top income decile emits more per capita in absolute than the lowest one.

This is especially manifest for gasoline consumption: richer households consume significantly more of it, but it represents less than 2-3% of their income, while it can reach more than 10% for poorer households.

Indeed, this can and should be offset with a full redistribution of the tax proceeds - either flat or targeted at lower income households - to compensate the inherent regressivity of carbon taxation.

Source: my PhD was on the distributional consequences of carbon pricing.

Carbon taxes are regressive but if it is all paid back as dividend then

a) poor people will end with more money than they paid

b) rich people will end with less money than they paid

c) no change in aggregate demand (although minor increase in velocity) so likely little additional inflation

So it still redistributed from rich to poor while disincentivizing carbon heavy processes.

Exactly. Coupled with the dividend, it is no longer regressive.

This page (https://citizensclimatelobby.org/household-impact-study/) has a nice chart showing the fees and where they come from for an average household in each income quintile in the USA. The expected fees for each quintile (under a $15/ton carbon fee) are $173, $219, $252, $292, $381. On another page on the same site, you can find that the expected dividend (which just depends on the number of adults/children in the household) is $288.

The central point is that the rich can also afford to pay for their supposed “orders of magnitude more carbon”.

They can do that with other taxes. I don't see the point here.

If we take a flat percentage of the spending and give everyone the same fixed amount, poorer people will profit more than rich people.

If you take a flat percentage small enough that poor people can afford it it's not even going to be close to enough for UBI. Sure poor people will profit more (if you assume they have a smaller CO2 footprint), but only at a scale of like a couple bucks.