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>

e2e/utils/e2e-setup.ts

@@ -0,0 +1,12 @@
+import fs from "node:fs";
+import path from "node:path";
+
+/**
+ * Clears the istanbul coverage output directory before the e2e run so stale
+ * coverage from previous runs is not merged into the report.
+ */
+export default function globalSetup(): void {
+  const dir = path.resolve(process.cwd(), ".nyc_output");
+  fs.rmSync(dir, { recursive: true, force: true });
+  fs.mkdirSync(dir, { recursive: true });
+}