bug(mat-datepicker): Datepicker cannot be closed when animating

### Is this a regression?

- [X] Yes, this behavior used to work in the previous version

### The previous version in which this bug was not present was

Introduced in https://github.com/angular/components/pull/25843

### Description

We have implemented a year-only-picker using mat-datepicker in listening to the (yearSelected) event and then closing the datepicker manually. However, if the user selects a new year fast enough the datepicker is still opening and animating (_isAnimating is true) and therefore the datepicker is not closed. This was introduced in https://github.com/angular/components/pull/25843

The problem is that the `_isAnimating` property and the `_animationDone` subject are both not exposed through public API so we cannot wait for the animation to be finished to close the picker. However, exposing it would be not a good solution as this would require us to have knowledge of the internals of the component to implement the solution. Rather, the datepicker should be fixed so the close event is scheduled for after when the animation is finished.

Thanks!

### Reproduction

StackBlitz link:
It simulates opening the datepicker and then closing it very fast through setTimeout to visualize the issue.
https://stackblitz.com/edit/datepicker-bug-material

### Expected Behavior

Either datepicker will close even if animating or datepicker will be scheduled for closing so it closes at the end of the animation.

### Actual Behavior

Datepicker is not closing while animating

### Environment

- Angular: 16.2.8
- CDK/Material: 16.2.7
- Browser(s): Chrome Version 117.0.5938.149 - all browsers.
- Operating System (e.g. Windows, macOS, Ubuntu): macOs 13.2.1 - all operating systems

Start with the linked StackBlitz reproduction and the Angular Material datepicker implementation, focusing on the close behavior while the picker is opening or animating. The fix is done when selecting a year quickly still closes the datepicker, either immediately or after the animation completes, and the behavior is covered by the relevant datepicker tests.

Written by the indexing model from the issue text.