e2e: Implement E2E Test to Validate UVE Mode Switching Content Integrity (#31456)

Task

This task involves implementing an end-to-end test to verify the fix for issue #31456, where the UVE content does not properly reflect changes when switching between modes using the dropdown.

The original issue showed that:

1. When swapping between modes using the dropdown in UVE, the iframe content was not updated correctly
2. The system appeared to use an older version of the PageAPI response
3. Users were unable to see their latest edits after mode switching

The test should validate that content changes persist and are displayed correctly when switching between different UVE modes.

Proposed Objective

Core Features

Proposed Priority

Priority 3 - Average

Acceptance Criteria

The E2E test should:

1. Successfully set up a test page in UVE with editable content
2. Make visible changes to the page content in one mode
3. Switch to a different mode using the dropdown
4. Verify that the content changes are correctly reflected in the new mode
5. Make additional changes in the new mode
6. Switch back to the original mode
7. Verify that all changes (from both modes) are correctly displayed
8. Include appropriate assertions to detect regression of this issue
9. Run successfully in the CI/CD pipeline
10. Include clear documentation of the test case and its purpose

Test should pass consistently and should fail if the original issue reoccurs.

External Links... Slack Conversations, Support Tickets, Figma Designs, etc.

No response

Assumptions & Initiation Needs

No response

Quality Assurance Notes & Workarounds

No response

Sub-Tasks & Estimates

No response

Start by reviewing issue #31456 and the UVE mode-switching flow described here. Set up a page with editable content, exercise the dropdown transitions in both directions, and add assertions that edits remain visible after each switch. Confirm the test runs consistently in the CI/CD pipeline and documents the regression it detects.