Since a single "300 problems" PDF is elusive, I will provide a to a high-quality alternative: "Problems in Relativity" by Prof. Matt Visser (Victoria University of Wellington) . This 90-page document contains over 250 problems with solutions, covering both special and general relativity, from basic to advanced.
The search for is a noble quest. While no single, universally recognized book bears that exact title, the content you seek is widely available. The combination of the Visser problem set, the Lightman textbook, and curated university collections will give you over 500 solved problems. Since a single "300 problems" PDF is elusive,
If you want, I can: