every time the rate is reported it is counting transactions. But you are right, technically when talking about "throughput" we should count payments not transactions and one tx can contain multiple payments.
I don't feel like checking the data (it's a lot of work), but my gut feeling tells me the number of transactions per block is going
down, despite Segwit, because of the batching which leads to much larger transactions. Counting transactions as a measure of Bitcoin's scaling would give the wrong result.