Why do only Xiaomi mobile phones receive short messages with avatars such as banks, and how can other mobile phones automatically display avatars?

Because the mobile phone has recorded the LOGO images of major banks. So there will be images when there are text messages and incoming calls. Of course, the same is true for contacts. When you store pictures of contacts, there will also be images during text messages and phone calls.

As for other mobile phones, that's because some information about the bank is not recorded. That's why it didn't.