The owl symbolizes wisdom and is the holy bird of Athena. The ancient Athens silver coin is the owl on the front of Athena on the back. Owls delivering letters were only relatively common in the Middle Ages, and while Harry's background is from the Enlightenment to the mid-industrial revolution, white owls are certainly not used. In the Middle Ages, wizards were persecuted by the church. Using magic to transmit information was easy to find. It was also dangerous to pass the information on the streets during the day.
You must know that if you go to the street to buy something, if you are caught, you will die, and if you are caught with important information, it will implicate a group of people. Then the information can only be transmitted by physical means at night. Owls have strong night vision, so they are used by some timid or cautious magicians to convey information. This is very safe. Using owls reduces the chances of being caught and exposed by the church. After all, it is difficult to catch a black owl in the dark.
The Middle Ages are not like modern cities that are brightly lit at night. If you have time to go to the countryside in backward areas, you will know what it is like at night. It's hard for the church to catch an owl. So at that time, the owl was used by some mages to pass the code. To know that the mage himself was caught with a secret code, the church can force the confession to find out the meaning. The owl was caught with a secret code and the church couldn't understand it.
