Is it legal for a restaurant manager to let a customer find out why the mistake happened?

It is entirely possible and very likely that neither the restaurant manager nor the waiter were aware of the mistake until you brought it to their attention. As long as the restaurant corrects the problem immediately, you wont suffer any harm and thus have no claim for damages. Kudos to you for keeping such a close eye on your account.

I don't think the restaurant is in control of this. I think this is the way your bank does this with your debit card. The problem this causes is that the bank usually holds that pending amount until it drops away. If you were counting on having that money to spend, you will not have it for a few days. You are asking if the restaurant is required to let you know that your bank does this. I do not see how the restaurant could notify you, since some banks do this and some do not. If your finances are very close to the edge where you need to have every dollar available to you, waiting for a pending charge to drop can be difficult. However, if you have sufficient money, the charge simply vanishes in a few days. It seems like it would be polite for the restaurant to let you know what happened and what is possibly going to happen with your bank, but I don't see how a restaurant can be required by law to warn you of the possible practices of your bank. You have my sympathy. I also have been concerned by pending charges such as this.