fix: Update Typescript testing rules and skills

[HassaanAhmadFarooqi]

Summary

• Used consistent test naming convention.
  • Updated tests examples accordingly.
• Added coverage details in e2e testing.
• Added more detailed files organization in playwright e2e-testing.
  • Added code examples related to these files.
• Updated playwright code examples to use better conventions.

Type of change

• New Claude agent
• New / updated Claude rules
• New / updated Claude skill
• New / updated Cursor rule
• Documentation update
• Other (describe below)

What was added / changed

As explained in Summary section.

Checklist

• File is placed in the correct directory
• Filename follows the naming convention for its type (kebab-case)
• YAML frontmatter is present and valid (for agents and skills)
• Content is accurate, concise, and free of typos
• No sensitive information (credentials, internal URLs, proprietary data) is included
• README updated if this addition warrants a mention

Related issues / references

None