Replace cypress with playwright (#1988)

## Launch Checklist

This PR replaces cypress with playwright.
<img width="1907" height="933" alt="image"
src="https://github.com/user-attachments/assets/b52075b3-eb3b-45dc-93dc-8c5e9cfd35dd"
/>

I hope this will make the end-to-end debugging and fixing easier due to
the async await support of playwright which is missing in cypress.

This is a pure refactoring change.

 - [x] Briefly describe the changes in this PR.
 - [x] Add an entry to `CHANGELOG.md` under the `## main` section.

---------

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Co-authored-by: Copilot Autofix powered by AI <62310815+github-advanced-security[bot]@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

.gitignore

@@ -33,10 +33,14 @@ node_modules
 public
 /errorShots
 /old
-/cypress/screenshots
 /dist/
 /desktop/version.go
 
+# Playwright
+/test-results/
+/playwright-report/
+/playwright/.cache/
+
 # IDE
 .vscode/
 .idea/