An error in iOS 14 means that not all alerts are sent to the user, and the problem is hardly fixed in 14.3.
You're not crazy
As usual, problems are discovered after the launch, so is the thing with 14 that already have problems with battery life.
It is iMessages or SMSs that are received, but which you are not always notified about. If you have noticed this problem yourself, it is not you, but iOS 14. At first, it was thought that it was the iPhone 12 series that there was something wrong with, but older models are also affected.
Try these tricks
It may seem like a strange "fix" to close the Messages app every time after sending a text message, but it's more complicated than just opening the messaging app to check if you've received a message.
It is also possible that removing an attached contact will fix the problem, so it's more worth a try.