Relocate e2e tests (#1989)

## Launch Checklist

Renames the e2e test and reduces changes as a preparation step from
playwright in the following PR:
- #1988

This is to keep as much history as possible.
<img width="1907" height="933" alt="image"
src="https://github.com/user-attachments/assets/b52075b3-eb3b-45dc-93dc-8c5e9cfd35dd"
/>

 - [x] Briefly describe the changes in this PR.

---------

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

vitest.config.ts

@@ -0,0 +1,11 @@
+import { defineConfig } from "vitest/config";
+
+export default defineConfig({
+  test: {
+    // Only the unit tests that live next to the source are run by Vitest. The
+    // e2e specs (*.spec.ts) are run by their own runner, and the component
+    // browser test is run separately.
+    include: ["src/**/*.test.{ts,tsx}"],
+    exclude: ["**/node_modules/**", "e2e/**", "**/*.browser.test.tsx"],
+  },
+});