bug(mat-datepicker): calendar with startAt attribute will not update on manual input

### Is this a regression?

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

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

_No response_

### Description

I built a mat-datepicker with startAt property (e.g. 01/01/2024).
Calendar starts as described in documentation at demanded calendar page.
If input value is changed, calendar will not update to desired page. (e.g. date is changed to 05/05/2024, calendar page is still on January 2024 instead of May 2024)

### Reproduction

StackBlitz link: https://stackblitz.com/edit/datepicker-property-error
Steps to reproduce:
1. Change input to any other date (e.g. 5/5/2024) either by typing or selection on calendar.
2. (Re-)Open calendar.

### Expected Behavior

Calendar should switch to page of desired month (e.g. May 2024).
startAt property should only set initial date and react accordingly to changes.

### Actual Behavior

Calendar does not change its page according to the input date. It remains on startAt date.

### Environment

- Angular: v17
- CDK/Material: 17.3.1
- Browser(s): Chrome, Firefox
- Operating System (e.g. Windows, macOS, Ubuntu): Windows

Start by reproducing the behavior in the linked StackBlitz and inspect the mat-datepicker entry point for how startAt and manual input affect the displayed month. Verify typing or selecting a new date, then confirm that reopening the calendar shows the month of the input date while startAt only controls the initial page.

Written by the indexing model from the issue text.