Preserve which page of the embedded live demo the user is looking at

### What feature do you want to see added?

Feedback indicates it'd be beneficial to preserve which page of the live demo the user was looking at when they refresh the page or update the prototype. This only applies to the embedded live demo.

### Why do you want this feature? Does it solve a problem?

When the user reopens or updates a prototype, they are taken back to the first page of the embedded live demo. This can be frustrating when they were previously looking at a particular page they just updated.

### How should the feature be implemented?

Needs to be user-specific, likely with the session data. Consider how to record when the live demo page changes, can this be done with the existing requests (e.g., when the user clicks "next" or "reset demo") rather than having to send additional requests?

### Additional context (if applicable)

_No response_

Start by tracing the embedded live demo's page navigation and the session data used when a prototype is reopened or updated. Check whether existing requests for actions such as "next" and "reset demo" can record the current page without additional requests; done means the user-specific page is restored after refresh, reopening, or updating the prototype.

Written by the indexing model from the issue text.