Is the SUNSYNK-SG01HP3-EU-AM2 SUNSYNK-12K-SG01HP3-EU-AM2 compatible with the Sunsynk CHNT DDSU666 (1ph 80A)?

Yes — listed by the manufacturer.

The manufacturer's published pairing data lists these together.

▦Manufacturer's compatibility listListed together in the manufacturer's published pairing data. A cited document reference is being added as datasheets are processed.