Is authenticated encryption unnecessary if the message is digitally signed?
Yes, message authentication can be omitted when using an appropriate digital signature on the ciphertext.

A digital signature hashes the message, then encrypts the hash with a nonce and asymmetric key, which makes the security similar to HMAC.

The reason authenticated encryption is preferred is that it is generally less computationally expensive than a digital signature, and easier to build a MAC construct that is side channel resistant.