Using Claude Code I'll often prompt something like this:
"Start a python -m http.server on port 8003 and then use Playwright Python to exercise this UI, there's a console error when you click the button, click it and then read that error and then fix it and demonstrate the fix"
This works really well even without adding an extra skill.
I think one of the hardest parts of skill development is figuring out what to put in the skill that produces better results than the model acting alone.
Have you tried iteratively testing the skill - building it up part by part and testing along the way to see if the different sections genuinely help improve the model's performance?