Granted, LN will aggregate transactions together, but the decentralized nature of LN will not allow scaling to reach "visa" levels.
Although in reality there are few LN node with lots of channel and big capacity.
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 idea.
Not exactly what you want, but those website show TPS based on mempool.
https://blockchair.com/bitcoin/charts/transactions-per-secondhttps://www.statoshi.info/d/000000006/transactions?viewPanel=6&orgId=1