Hello,
We do plan to implement SHA3, HMAC-SHA3 and KMAC. But we don't know yet when that will happen. As usual, the bottleneck is review bandwidth (we have had two independent contributions of SHA3!).
Our roadmap (https://mbed-tls.readthedocs.io/en/latest/project/roadmap/) unfortunately doesn't list SHA3, but the “EdDSA” item includes Ed448 which requires SHA3. I'll see about clarifying that since SHA3 is useful for other things as well.
Note however that SHA3 support in X.509 and TLS, in places where SHA2 is currently supported, is not currently on the roadmap, as far as I'm aware.
Best regards,