You don't need state surveillance or tracking purchases. You just need to get to the source of the problem. Hydrocarbons leaving the ground.

At the hydrocarbon level, it's much easier to track. Oil and gas is mostly extracted by very large corporations and transported by large infrastructure. You don't care what happens to it once you've produced it - but you do need to put a levy on the hydrocarbons before they're sold on. The people who use those hydrocarbons all have higher costs which pass on to customers.

The biggest problem is international borders. If another country isn't applying carbon tax, then you need to make an estimate of the embodied energy of a product at the point of import. Or encourage them to tax carbon. But neither of those require surveillance. Once the product has been imported, you don't care who buys or sells it because the tax is already paid.

For a carbon tax, I think you only need to track imports, and domestic extraction of coal, petroleum, and natural gas.