Not only for chat apps and email services, literally all user data on servers should be encrypted with the decryption key only on the user's devices. It should basically be impossible to identify a user based on the data that a service provider has.

The idea is similar to that of ZeroDB, but it extends beyond databases to everything related to a user such as files related to a user.

The literature for Protonmail looks really good, thanks for the tip. Can you recommend them service-wise?

I started using Protonmail 2 weeks ago and I am quite satisfied (planning to migrate all my communication from Gmail to Protonmail). It does feel slower than Gmail (because of the decryption, but that's not that much of a problem). Also, you have to use their own app, it cannot be connected to a mail client, that's a bit of a downside, but I suppose I will be willing to make that compromise.