In the past it was mostly the second, but now its the first.

It’s all an immutable ledger, where the “account balance” is just a sum of all transactions on the account…

disclaimer: I don’t work in finance at all

it all just lives in a bunch of csv files on a few people’s PCs and every night a 62 year old man copy pastes it together and checks everything and then uploads it to some old mainframe. he is the only one who knows how to do that job.

I cannot tell if this is a serious comment.

It isn't, but it's not that far from being a serious comment.

The old man has an ancient PC choking on dust under his desk that runs a QWS3270 terminal that updates the mainframe directly. If it's a big bank, the bank owns the mainframe. If it's a small bank, a vendor (probably Fiserv) does.

Source: I've consulted for a lot of banks.

I remember one bank used to, and it was big news, process all deductions from accounts, then issue overdrawn penalties, then any deposits. So if you had $500 in your account, then deposited $500 in cash, then withdrew $501, you would be overdrawn and assessed a penalty. Oh and it was a very major bank (in the US).

If you're interested in this topic, you may want to read through some of the Bits about Money essays/newsletters: https://www.bitsaboutmoney.com/

Look into Flexcube docs to more fully answer your questions. It's a reasonably well established core banking product, or series of products.