Large Language Models (LLMs) are increasingly used in software engineering research, offering new opportunities for automating repository mining tasks. However, despite their growing popularity, the methodological integration of LLMs into Mining Software Repositories (MSR) remains poorly understood. Existing studies tend to focus on specific capabilities or performance benchmarks, providing limited insight into how researchers utilize LLMs across the full research pipeline. To address this gap, we conduct a mixed-method study that combines a rapid review and questionnaire survey in the field of LLM4MSR. We investigate (1) the approaches and (2) the threats that affect the empirical rigor of researchers involved in this field. Our findings reveal 15 methodological approaches, nine main threats, and 25 mitigation strategies. Building on these findings, we present PRIMES 2.0, a refined empirical framework organized into six stages, comprising 23 methodological substeps, each mapped to specific threats and corresponding mitigation strategies, providing prescriptive and adaptive support throughout the lifecycle of LLM-based MSR studies. Our work contributes to establishing a more transparent and reproducible foundation for LLM-based MSR research.