Why didn't the bank inform you by SMS when shopping with a credit card in Hong Kong?

One possible reason is that small consumer banks do not provide information services.

It is also possible that your mobile phone is not roaming in Hong Kong and Macao, and you can't receive it, or the information is delayed because of the cross-border network.

It is also possible that your credit card issuer did not provide SMS notification at all.

Actually, a receipt is enough. This is the best proof.