The cost of a Bitcoin transaction doesn't scale respective to the amount that is being sent, but according to the amount of data that the transaction occupies on the blockchain. Bitcoin transactions can perform multiple payments, so the transaction count is also not necessarily a good proxy for the count of payments in a block. If the hypothetical banks wanted to use Bitcoin for settlement, they could probably settle up once per day where each bank pays all of the recipient banks in one or a few transactions and it would take very little blockspace. If they make very frequent payments that need immediate settlement, the hypothetical banks should probably onboard to the Lightning Network and establish direct channels between each other, supported by infrequent on-chain transactions to rebalance their payment channels.
Back to your main question: the Bitcoin blockchain produces about one block every 10 minutes. Since the activation of the segwit softfork, blocks are limited to 4,000,000 weight units (before segwit: 1,000,000 bytes) which usually amounts to 2,000–4,000 transactions. Over the entire history of Bitcoin, blocks have had between 1 and 12,239 transactions.
There is a big range to the count of transactions that fit into a block, because transaction weight is variable depending on the number of inputs spent and number of outputs created by a transaction. A minimal common transaction specimen would perhaps be a P2WPKH input and two P2WPKH outputs which weighs around 562 weight units (140.5 vB). However, the largest standard transactions are permitted to weigh up to 400,000 weight units (100,000 vB).
The transactions before segwit had a higher weight. A transaction with one input and two outputs of the then most common default type P2PKH has a size of 904 WU (226 B), about 1.61× the size of a P2WPKH transaction. So, if everyone would have used single input two output single-sig transactions, we would have assumed the input count of transactions also to increase by about a 1.6×. However, since then, the average outputs per transaction and inputs per transaction have each increased from about 2.5 in August 2017 to around 3.3 today, generally increasing the size of transactions we see. The number of payments per transaction has increased even more from 1.5 to about 2.6.
So, it's a bit meaningless to compare the transaction count before segwit and after segwit, because the nature of transactions has changed more than the count of them, while the payments per day have gone up dramatically.
Take for example the recent new biggest block 748,918:
It was a full block with 3,993,415 WU, but had only 202 transactions spending a total of 9,468 inputs and creating a total of 391 outputs.
On the other hand, block 367,853, the block with the highest transaction count even predated segwit activation:
It had a transaction count of 12,239 consuming 13,176 inputs and creating 12,917 outputs.
Since transactions can pay multiple recipients, the count of transactions is also not necessarily a good proxy for the number of payments performed in a block. when there are many transactions performing batched payments.
Block 409,069 only had 368 transactions spending 1,387 inputs, but created 23,642 new transaction outputs.
For comparison, the current block 753,191
had 3,543 transactions spending a total of 6,366 inputs and creating 12,529 new outputs.