When I cancelled my card, the customer service told me that I would have to wait 34 days to stop using it, and I would officially stop using it without a new account.

Then the explanation is that some credit card transactions, such as handling fees and interest, will be recorded on the billing date, and there are some authorized transactions. Merchants will have a certain time to ask for money, and 34 days can cover almost the whole billing cycle, so this is a buffer time for the bank to officially cancel your card.