AEAD implies the support for additional Authenticated Data (AD); this is just Encrypt-them-MAC, which is a good construction for authenticated encryption, but it's not AEAD (by definition).
If you want an AEAD, I designed one based on ChaCha20 and BLAKE3 as a proof-of-concept a while ago: https://github.com/soatok/experimental-caead
The important details:
1. You need to split a single key into 2 distinct keys (1 for [X]ChaCha, 1 for BLAKE3).
2. You need a canonical way to feed the ciphertext and AAD into BLAKE3.
3. You need to ensure your MACs are compared in constant-time.
The GitHub repository I linked above does all this.