feat: Enhance ion-router-outlet to Support ViewTransition API for Improved Page Transitions

### Prerequisites

- [x] I have read the [Contributing Guidelines](https://github.com/ionic-team/ionic-framework/blob/main/docs/CONTRIBUTING.md#creating-an-issue).
- [x] I agree to follow the [Code of Conduct](https://ionicframework.com/code-of-conduct).
- [x] I have searched for [existing issues](https://github.com/ionic-team/ionic-framework/issues) that already include this feature request, without success.

### Describe the Feature Request

Integrate support for the [ViewTransition API](https://developer.mozilla.org/en-US/docs/Web/API/View_Transition_API) within Ionic's ion-router-outlet component. This enhancement would enable developers to utilize the [ViewTransition API](https://developer.mozilla.org/en-US/docs/Web/API/View_Transition_API) for seamless and customizable view transitions in Ionic applications.

### Describe the Use Case

Currently, developers aiming to implement the [ViewTransition API](https://developer.mozilla.org/en-US/docs/Web/API/View_Transition_API) encounter compatibility issues with ion-router-outlet. This limitation restricts the ability to create smooth and native-like transitions between views, which is essential for enhancing user experience in modern applications. By incorporating support for the [ViewTransition API](https://developer.mozilla.org/en-US/docs/Web/API/View_Transition_API), developers can achieve more refined and customizable transitions, leading to improved application aesthetics and usability.

### Describe Preferred Solution

Enhance the ion-router-outlet component to support the [ViewTransition API](https://developer.mozilla.org/en-US/docs/Web/API/View_Transition_API), ensuring compatibility. This could involve updating the component's internal handling of view transitions to accommodate the API's capabilities.

### Describe Alternatives

_No response_

### Related Code

_No response_

### Additional Information

_No response_