Under the current carbon pricing scheme, there is no such thing as purchasing of carbon credits. This might be the case under a cap and trade system, which currently only exist in places like Quebec and California (and formerly Ontario). Additionally, if corporations were exempt, there would be no need to buy carbon credits.
There are special areas such as home heating where there is a temporary hiatus on the carbon pricing.
The carbon tax rebates apply uniformly. But remember that carbon pricing punishes those who heavily rely on carbon based fuels (e.g. people with multiple vehicles, homes, etc).
Carbon pricing is not intended to redistribute wealth. So the point about the upper class paying a lesser percentage of their wealth is not relevant and we also don't have evidence of this.
I am not denying that the upper class may pay a lesser percentage of their wealth. What I am saying is that even if it is true, this is not relevant to the discussion on carbon pricing because that is not the objective in the first place.
The point of the carbon pricing is to mitigate the effects of the climate crisis.
Wealth redistribution is well deserving of its own discussion. However, on its own wouldn't be a very effective tool to address the climate crisis as it does not hit the core of the issue, which is greenhouse gas emissions.