Taxes are a cost from a business accounting perspective. Costs are not borne by the business but paid for by their customers in a manner which is usually obscured to them. A “carbon” tax would effectively be a tax on all goods and services that use energy (all of them).
Now my understanding (when I’ve raised this cost of governance issue with advocates prior anyway) of a lot of carbon tax proposals is that the taxes paid would be remitted back to taxpayers or citizens in some way in a kind of Robin Hood-like manner rather than actually used to cover the cost of government, but this doesn’t actually accomplish anything and I disagree with that kind of scheme on prudential grounds (inappropriate use of tax authority). In any case it would be cash seized from someone who earned it first. A power plant doesn’t emit hydro-carbons needlessly, it emits them as a function of a customer downstream paying for it: to power your refrigerator or to pay for the manufacture of the phone you purchased.
Whether you are levying the tax against the business operating the plant, the customer at the point of sale or any and all of the intermediaries, what you are effectively doing is raising business costs no matter how you phrase it or rhetorically justify it. This informs the final product and service price, so if costs go up including taxes, you should also expect prices to go up.