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-teardown.ts

@@ -0,0 +1,23 @@
+import fs from "node:fs";
+import path from "node:path";
+import { execFileSync } from "node:child_process";
+
+/**
+ * Merges the per-test istanbul coverage chunks collected in `.nyc_output` into a
+ * report (configured by `.nycrc.json`) once the whole e2e run has finished.
+ */
+export default function globalTeardown(): void {
+  const dir = path.resolve(process.cwd(), ".nyc_output");
+  const hasCoverage = fs.existsSync(dir) && fs.readdirSync(dir).some((f) => f.endsWith(".json"));
+  if (!hasCoverage) {
+    console.warn("No coverage data collected; skipping coverage report.");
+    return;
+  }
+  try {
+    execFileSync("npx", ["nyc", "report"], { stdio: "inherit" });
+  } catch (error) {
+    // Don't fail the whole run if the report can't be generated (e.g. when
+    // running against a container whose source paths differ from the host).
+    console.warn("Failed to generate coverage report:", error);
+  }
+}