Smooth transition between closing one modal and opening another

[EugeneYaremenko]

Currently, when one modal closes and another one opens immediately after, the transition between them appears abrupt. This causes a noticeable flicker: the first modal disappears instantly, and the next modal is rendered only afterward.

Expected behavior:
Provide a way to achieve a smooth, seamless transition from one modal to another. For example, by allowing the outgoing modal to play its closing animation fully before the next modal starts opening.

[max-mykhailenko]

The <ViewTransition /> API is currently available only in React’s Canary and Experimental channels, so we should wait.