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>

cypress.config.ts

@@ -10,6 +10,7 @@ export default defineConfig({
   },
 
   e2e: {
+    specPattern: "e2e/**/*.spec.ts",
     setupNodeEvents(on, config) {
       // implement node event listeners here
       require("@cypress/code-coverage/task")(on, config);