A tigger is the only valid option if you want accurate notification . Something that runs from time to time may work in some very specific scenarios, but "always" will perform less. Unless what you want is not well checked from time to time and the update cycle is very high, which does not seem to be the case.
The trigger ensures that any change in the bank notifies you. You might want this. You may wish to have notifications from time to time. They are different semantics.
The trigger has a cost for each operation; if you do not need these notifications on time, it may be a cost.
Check lots has an extra single cost and will make unnecessary operations, but relieves each update and can choose to do so in non-critical hours. It will not change much, but in large volumes it can make a difference. Can you leave the notification for later without any problems? Are you going to do this often? So I doubt it's a good option.
Take a test to see which works best for you. It is not easy to choose, depends on the need and how to implement. The danger is in the detail.
This site here chooses to update certain things in batch, but some are made on time. It depends on what you want and how much it affects the established performance metric.
In some databases better options than using cron
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Of course, it depends on the architecture of your solution. I'm considering what you want to do in the database. In general I'd rather do it on another layer.