Write a JS script that creates a pop-up with a responsive modern style UI that shows users the color palette values from the active web page and automatically displays the color palette values in hexadecimal, RGB, and HSL formats. Show the color code text values for each, in small black bold text under each color box. The code should be efficient and respectful of user privacy and security, including suitable error handling for potential issues such as browser compatibility or failure to pick a color. Inject the function into the code of the active web page. The script should execute immediately without requiring any additional user interaction.