For open source messengers, you can check whether they actually encrypt your messages and whether the server has access to your encryption keys but what about WhatsApp? Since it’s not open source, you can’t be sure that the encryption keys aren’t sent to the server, right? Has there been a case where a government was able to access WhatsApp chats without reading them from the phone itself?
Everything I’ve ever heard about government cryptography from people close to me is that the government (FBI, military) is wildly far ahead of what’s available publicly. I wouldn’t count on anything you do on the Internet to be truly private.
That was at times of DES. Cryptography that is used today is proven to be complicated enough that it’s unbreakable unless the government got quantum computing working at sufficient skale.
Like others wrote, attacks will happen when the messages are received and decrypted.