This research examines how performance-approach and mastery-approach goals mediate the relationships between teacher and peer support and various emotions, namely Foreign Language Enjoyment (FLE), technology anxiety, boredom, as well as the state of flow among Chinese university English as a Foreign Language (EFL) learners in Informal Digital Learning of English (IDLE) environments. It also investigates whether these relationships differ for learners using large language models (LLMs) compared to those who do not. The study, which analyzes data from 1,685 Chinese EFL learners using Partial Least Squares Structural Equation Modeling (PLS-SEM), shows that teacher support significantly affects emotions, whereas peer support specifically impacts FLE and technology anxiety. Performance-approach and mastery-approach goals mediate their relationships, except for boredom. Both types of support significantly predict flow, with approach goals mediating the effects, and only FLE positively impacts flow. A multigroup analysis highlights significant variations across groups in the effects of teacher support on mastery-approach goals, the influence of teacher support, peer support and performance-approach goals on technology anxiety, and the impact of teacher support and FLE on flow. These results provide valuable insights for improving educational practices and policies by fostering supportive climates and aligning goals with LLM technologies.