Freelance workers must continually acquire new skills to remain competitive in online labor markets, yet they lack the organizational training, mentorship, and infrastructure available to traditional employees. Generative AI-powered tools like ChatGPT are reshaping market skill demands while also offering new forms of on-demand learning support to meet those demands. Despite growing interest in AI-powered learning tools, little is known about how freelancers actually use these tools to learn, the challenges they encounter, and how generative AI for learning interacts with precarity and competition in platform-based work. We present a mixed-methods study combining a survey and semi-structured interviews with freelance knowledge workers. Grounded in self-directed learning theory, we examine how freelancers integrate generative AI tools into their learning practices. Our findings show that freelancers increasingly rely on generative AI to structure learning and support exploratory skill acquisition, but do not treat it as their primary learning resource due to inconsistency, lack of contextual relevance, and verification overhead. We identify a shift from learning as growth to learning as survival, where upskilling is oriented toward immediate market viability rather than long-term development. We also surface a structural challenge we term invisible competencies, in which workers acquire skills through generative AI tools but lack credible ways to signal or validate these skills in competitive freelance markets. Based on these insights, we offer design recommendations for generative AI-powered learning tools for freelancers.