Context: Test Automation (TA) techniques are crucial for quality assurance in software engineering but face limitations such as high test suite maintenance costs and the need for extensive programming skills. Artificial Intelligence (AI) offers new opportunities to address these issues through automation and improved practices. Objectives: Given the prevalent usage of AI in industry, sources of truth are held in grey literature as well as the minds of professionals, stakeholders, developers, and end-users. This study surveys grey literature to explore how AI is adopted in TA, focusing on the problems it solves, its solutions, and the available tools. Additionally, the study gathers expert insights to understand AI's current and future role in TA. Methods: We reviewed over 3,600 grey literature sources over five years, including blogs, white papers, and user manuals, and finally filtered 342 documents to develop taxonomies of TA problems and AI solutions. We also cataloged 100 AI-driven TA tools and interviewed five expert software testers to gain insights into AI's current and future role in TA. Results: The study found that manual test code development and maintenance are the main challenges in TA. In contrast, automated test generation and self-healing test scripts are the most common AI solutions. We identified 100 AI-based TA tools, with Applitools, Testim, Functionize, AccelQ, and Mabl being the most adopted in practice. Conclusion: This paper offers a detailed overview of AI's impact on TA through grey literature analysis and expert interviews. It presents new taxonomies of TA problems and AI solutions, provides a catalog of AI-driven tools, and relates solutions to problems and tools to solutions. Interview insights further revealed the state and future potential of AI in TA. Our findings support practitioners in selecting TA tools and guide future research directions.