How to manually verify whether a software is truly end to end encrypted?

recently i have been interested in end to end encryption and how it works
from what i have read, when a message is end to end encrypted then first a public and private key are first generated which are used to encrypt and decrypt respectively the message only on the client side
in theory i get how this works but i want to see and observe how this happens in real time, is there a way or a tool that …

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