The sixth generation (6G) of mobile networks presents transformative possibilities but also introduces significant security challenges. This paper surveys the state-of-the-art in 6G security from 2020 to 2025, highlighting advancements, challenges, and potential solutions. We distinguish our survey by offering a comprehensive, cross-layer analysis of the role of artificial intelligence (AI) in both enabling and threatening 6G security. First, we outline the technological foundations and core features of 6G and 6G AI, emphasizing their implications for security. We then explore how AI can be leveraged for both offensive and defensive purposes across the infrastructure, network service, and application layers. Our study categorizes AI-driven threats and countermeasures and provides a structured analysis of five key security frameworks. We further examine how quantum-enhanced technologies contribute to securing AI in 6G environments. Finally, we identify open research questions and present key lessons learned to guide future research in building resilient and trustworthy AI-integrated 6G networks.