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>

AGENTS.md

@@ -24,22 +24,22 @@ The project type checked and built with:
 npm run build
 ```
 
-To run the tests make sure that xvfb is installed:
+Install the Playwright browser (first time only):
 
 ```
-apt install xvfb
+npx playwright install --with-deps chromium
 ```
 
-Run the development server in the background with Vite:
+Then run the end-to-end tests (Playwright starts the dev server automatically):
 
 ```
-nohup npm run start &
+npm run test
 ```
 
-Then start the Cypress tests with:
+Run the unit and component tests with Vitest:
 
 ```
-xvfb-run -a npm run test
+npm run test-unit
 ```
 
 ## Pull Requests