bug: Nav does not inherit the mode to page components

### Prerequisites

- [X] I have read the [Contributing Guidelines](https://github.com/ionic-team/ionic-framework/blob/main/.github/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 report this problem, without success.

### Ionic Framework Version

- [X] v4.x
- [X] v5.x
- [X] v6.x
- [ ] Nightly

### Current Behavior

When manually applying the mode to `ion-nav`, the resulting page components pushed into nav do not inherit the specified mode. Additionally, page transitions for the nav to not take into account the manually assigned mode.

This behavior has existed for a long time in Ionic. Changing this behavior should be consider a breaking change and handled during a major version of Ionic.

Split from: https://github.com/ionic-team/ionic-framework/issues/24264

### Expected Behavior

When using `` all page components that are pushed to the nav should default to the manually specified mode, `ios`. The resulting page transitions should also inherit the mode.

### Steps to Reproduce

1. ``
2. Preview in MD mode
3. Push a view
4. Observe: Page components are not iOS
5. Observe: Page transition is not iOS

### Code Reproduction URL

_No response_

### Ionic Info

N/A

### Additional Information

_No response_

Start with the ion-nav implementation and reproduce the issue using the reported mode="ios" steps in an MD-mode preview. Trace how the nav mode is applied to pushed page components and page transitions; done means both use the manually assigned ios mode, with behavior treated as a breaking change.

由索引模型根据 Issue 内容生成。