Most message encryption schemes don't use this alone. This is a Key Encapsulation Method (KEM) and it's designed as a way to exchange key information between two parties, much like Ephemeral Diffie Hellman (EDH) with Ed25519. However many are using Kyber _with_ Ed25519 as a hybrid system. The keying material generates using both schemes are fed into a Key Derivation Function (KDF) to generate a shared symmetric key and then uses AES-GCM or ChaCha20Poly1305 to encrypt any subsequent messages.

The reason why we want Kyber is that it's supposed to be post-quantum secure. Ed25519 does not have evidence that it is post-quantum secure, so using a hybrid system does at least guarantee that your scheme is post-quantum ready. The reason you don't immediately switch to Kyber is in case of dodgy initial Kyber implementations, or unknown protocol issues we have not yet discovered.

They use it for key exchange. That removes the part that quantum computing will break easily.

AES is still safe. It is a replacement for public key crypto schemes, like Ed25519.