Various AI technologies have been extensively introduced in language learning, showing positive impacts on students' learning, especially on their classroom-based engagement. Yet, AI's comprehensive affordances as well as influences across different cohorts of student engagement remain underexplored. Given this, the current study, employing structural equation modelling (SEM), delineated the factor structures and predictive relationships of AI affordances and student engagement. Besides, to clarify the variations across different engagement subgroups, the study also explored latent profiles of student engagement and their moderating effects through latent profile analysis (LPA). SEM and LPA were conducted using AMOS 23 and Mplus 8, respectively. The participants comprised 408 undergraduate students from various universities in China, who have engaged in English as a Foreign Language (EFL) learning within AI-empowered classroom environments. Factor analysis indicated that both AI affordances and student engagement exhibited two second-order factor structures. AI affordances were categorised into four dimensions: convenience, interactivity, personalisation and social presence. Student engagement was also divided into four dimensions: cognitive, behavioural, emotional and social engagement. Additionally, AI affordances significantly affected student engagement, with this impact being moderated by different student engagement profiles. Student engagement was segmented into three sub-groups: non/low engagement, high engagement and moderate engagement. Therein, AI affordances showed a notable effect on the non-/low engagement group. These findings provide a solid foundation for future research in the integration of AI technologies with language learning.