CO2 footprint per bitcoin transaction
I did some napkin math based on your data. At 4 tx/s and 8GW, that is 2GWs per transaction. 0.5kg/kWh is around 139kg/GWs. Thus each transaction is around 278kg. Looks like we reached the same answer. 

But is this the carbon footprint of one Bitcoin transaction? To put it differently, if there was a global carbon tax, would it makes sense to charge for 278kg per transaction? Probably not. In fact, almost certainly most of the tax would just apply to the electricity bill of Bitcoin miners, which is split between hashing for the block reward and processing transactions.

There are roughly 2000 transactions per block. Each transaction costs roughly \$1. The block reward is 12.5 Bitcoins as of now. At \$8200 per Bitcoin, roughly $\$2000/(12.5\space\text{BTC} \times \$8200/\text{BTC} + \$2000)=0.0191$ or 2% of a miner's electricity bill goes to transaction processing. So perhaps it makes more sense to say that each transaction costs around $278\space\text{kg} \times 0.02=5.56$kg of carbon.

So what about the rest of the carbon? In some sense, the main job that PoW does is preserving the integrity of existing token balances. The block reward is seniorage. This a similar principle to how central banks print more money and thus reduce the value of existing bank notes and coins. As of now there are close to 18 million Bitcoin in existence. Continuing with your carbon emission numbers, each Bitcoin holder that isn't transacting is then responsible for $((8/(18 \times 10^6)) \times 139) \times 0.98=0.000060542$kg of carbon per second per Bitcoin or 5.23kg of carbon per day per Bitcoin.