欸 has multiple pronunciations and meanings that vary by tone: ēi = response/agreement, éi = surprise/puzzlement, ěi = mild disapproval, èi = yes/agreement. In informal speech and texting, 欸 is interchangeable with 诶. Context and surrounding text determine the intended reading.
欠 (the indexing radical) pictures a person opening their mouth wide, exhaling, yawning, sighing. Perfect anchor for an interjection: 欸 is a sound made on a short out-breath. Same radical in 歌 (sing), 欢 (cheer), 叹 (sigh).
矣 supplies the sound stem. 欸 has multiple readings (āi, éi, ěi, èi) for different attention-getting and reaction tones, all riding on phonetic shifts from the 矣-stem core. Pure phonetic role, the classical particle meaning of 矣 is not active here.