The animation re-started on the right side of the screen and the iframe has lost all its state. ☹

While transition:persist generally works fine and can keep the state of almost all HTML elements, animation state and iframe state are its Achilles' heel.

Let's try something else when transitioning to the next page: Again, enter a search term in the iframe, then wait for the circle being near the left edge of the screen, then hit the link to the next page. The iframe should keep its state now.