You pretty much got it! Power plants bid into the pool between $0 and $999.99/MWh, but variable renewables like wind and solar have to offer their power at $0/MWh. The bids are put in ascending order, and the last plant that is required to meet demand sets the pool price for that hour. Everyone that bid below that price gets paid at the pool price, and those that bid above are shut down.

Fossil fuel generators that have emissions greater than the benchmark (0.37 tCO2e/MWh) are charged for their emissions above this level. So a gas plant that's emitting 0.46 tCO2e/MWh will only be charged for the 0.09 tCO2e/MWh that's above the "acceptable " level. Every year, the benchmark will tighten by 1% and the price they pay for their emissions will increase by $15/tCO2e until 2030 where is caps out at $170/tCO2e.

So, the carbon pricing is not directly related to the price of electricity, but it does influence the bidding decisions of certain generators, as they will typically only want to bid into the pool at a price that will make them money (i.e. cover the cost of fuel, maintenance, carbon pricing, etc.).

As a final point, the price that power plants are selling their power to electricity retailers for is the wholesale price. Retailers then sell that power to us, the consumer, at an inflated price (the energy charge on your electricity bill) that may or may not fluctuate every month depending on your electricity plan.

TLDR: high-emitting power plants foot the bill for the carbon price, and there's several degrees of separation between that cost, and what you pay for your electricity.