bug: ion-datetime after canceling and reopening the date shows incorrectly

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### 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 report this problem, without success.

### Ionic Framework Version

v8.x

### Current Behavior

After canceling out of a datetime component and reopening the view you see the incorrect date displayed as selected even though the value is the correct one.

### Expected Behavior

After canceling out of the datetime view and reopening it the active date should show the actual value and not the canceled one.

### Steps to Reproduce

1. open the datetime view and select a new date and click ok. the button shows correctly
2. reopen the datetime view and select another date but click on cancel this time. the button still shows correctly.
3. reopen the datetime view you see the incorrect date displayed as selected even though the button shows the correct one (and the underlying value is the correct one).

### Code Reproduction URL

https://stackblitz.com/edit/invgnexq

### Ionic Info

Ionic:

Ionic CLI : 7.2.1 (/usr/local/lib/node_modules/@ionic/cli)
Ionic Framework : @ionic/angular 8.7.9
@angular-devkit/build-angular : 20.3.9
@angular-devkit/schematics : 20.3.9
@angular/cli : 20.3.9
@ionic/angular-toolkit : 12.3.0

Capacitor:

Capacitor CLI : 7.4.4
@capacitor/android : not installed
@capacitor/core : 7.4.4
@capacitor/ios : not installed

Utility:

cordova-res : not installed globally
native-run : 2.0.1

System:

NodeJS : v22.19.0 (/usr/local/bin/node)
npm : 11.6.2
OS : macOS Unknown

### Additional Information

_No response_

Start by running the linked StackBlitz reproduction and exercising the ion-datetime cancel-and-reopen sequence described in the issue. Trace the ion-datetime implementation and existing coverage for its selected date and cancel behavior; done means reopening shows the underlying value rather than the canceled date.

Written by the indexing model from the issue text.