I am a firm believer that there are many privacy techniques you should focus on before encrypted messaging because they will offer you much more “bang for your buck,” things like good passwords, two-factor authentication, and even encrypted email. That said, I still believe that encrypted messaging is a critical part of a well-rounded privacy and security strategy. While the vast majority of our day-to-day conversations may be benign, it can still offer a lot of insight into who we are as people – our routines, likes, and personal thoughts. This information – mundane or not – is worth protecting.
Element X (Matrix client). Basically anything that offers F-Droid or open source release will have builds without built-in notifications. Play Store/App Store builds requires using native notification systems.