The transaction rate is a matter of public record, and can be seen here for instance. It varies, but seems to typically be in the range of 200k-300k transactions per day. (This is close to the theoretical maximum, since the protocol is limited to 576M "weight units" of transaction data per day, and simple transactions require about 1k.)
The cost of mining can only be roughly estimated. One method, used by the paper linked in this question, is to compare the current hashing difficulty level (which is public) to the efficiency of current mining hardware. Another method is to start from the current mining reward (which is public) and the assumption that miners are not mining at a dramatic profit or loss (which is reasonable because of the way the hashing difficulty auto-adjusts). As far as I know these give similar results.
However (and this is the main reason I'm writing this answer), dividing the second number by the first to get a "cost per transaction" makes little sense, because there's little cause-and-effect relationship between them. There is some connection, because some of the mining reward comes from transaction fees, but currently it's less than 10% (based on this chart and the fact that the current coinbase reward is about 900 BTC/day), so even a dramatic drop in transaction rate could be expected to have only a small effect on mining cost if all else was held equal. The total mining cost is much more closely tied to the price of Bitcoin, which is determined by trading on exchanges built on traditional databases, and not by on-chain transactions.
There seems to be a common belief (probably exacerbated by the unfortunate term "mining") that bitcoins themselves are cryptographic objects that must be "found", and that the energy cost of bitcoin is somehow related to this. For example, a comment on this question says
Worth noting that the blockchain algorithm is designed to get harder to mine as time passes (limited total bitcoins).
This is completely untrue. The mining difficulty is algorithmically adjusted so that one valid hash is found every ten minutes on average, which means that it's proportional to the amount of effort being spent on mining, which can go up or down. The difficulty has nothing to do with the contents of the block chain as such. It would be the same if the block chain had nothing to do with money, and instead contained episodes of This American Life, if the miners had some motivation to throw a similar amount of computing power at securing that information.
It is probably fair to say that Bitcoin has a high cost per transaction by design, because the maximum transaction rate is low by design and the proof of work must be expensive (in real money/natural resources) by design in order for the block chain to be secure. What isn't reasonable is the idea that any particular transaction that you submit to the network has a large carbon footprint that could have been avoided by not submitting it. If anything, reducing the transaction rate makes the problem worse. The problem of high environmental cost can only be solved by abandoning Bitcoin entirely or by fundamentally changing how it achieves its security (which would also amount to abandoning Bitcoin-as-it-stands).
The other answer said
Mind you, the "power consumption per transaction" metric includes not only the direct transactions but also the mining used to maintain the ledger.
As far as I can tell, this is also not true. The power-consumption analyses appear to consider only mining costs. Non-mining nodes consume some power verifying the actual contents of the block chain – which involves public-key cryptography and is entirely separate from the proof-of-work calculation – but I think that it's negligible in comparison to the proof-of-work cost. At least, power analyses seem to treat it as negligible.
