How many souls did the death of Jesus pay for?

Well, all of them — as many as believe in him.  See 1 Tim 2:5-6:

For there is one God and one mediator between God and men, the man Christ Jesus,  who gave himself as a ransom for all men—the testimony given in its proper time.

Like all uses of the word “all”, the question is, how much all is all? In this case, the answer is clearly “enough that we don’t need to worry about it not being enough”.

Some people have used verses such as the 144,000 out of Rev 7:4;14:3 to argue that there’s a limit to the number of the redeemed. Personally, I don’t think these numbers are supposed to be interpreted literally as numerical limits to the number of the saved, and even if they are, there’s no suggestion that any limit is due to Jesus not paying enough.

Actually, as far as I can tell, the Bible never uses the word “pay”, “paid”, etc., with regard to Jesus’ sacrifice. Although it did ransom us, there’s no suggestion that it was a payment for our debts. However, it did (thankfully) create grounds for God to forgive our debts.