dev(studio): add claude skills for e2e tests (#42266)

## I have read the
[CONTRIBUTING.md](https://github.com/supabase/supabase/blob/master/CONTRIBUTING.md)
file.

YES

## What kind of change does this PR introduce?

LLM configuration

## What is the current behavior?

No skills for E2E tests

## What is the new behavior?

Claude skill for E2E tests


<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

* **Documentation**
* Added comprehensive end-to-end testing guidelines for Studio
Playwright tests, covering test execution, environment setup, robust
selector patterns, common pitfalls, debugging workflows, and CI
troubleshooting.

* **Chores**
* Updated repository ignore settings so skills-related documentation
files are tracked and can be committed.

<sub>✏️ Tip: You can customize this high-level summary in your review
settings.</sub>
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

.gitignore

@@ -120,6 +120,8 @@ next-env.d.ts
 .claude/*
 !.claude/settings.json
 !.claude/scripts/
+!.claude/skills/
+.claude/skills/me-*
 CLAUDE.md
 
 #include template .env file for docker-compose