bug(Datepicker): setting value inside valueChanges doesn't update the UI

### Is this a regression?

I don't know if this was working at some point or not

### Description

I am using reactive forms to get/set values from a datepicker and I noticed that if I set a date manually, inside the valueChanges event based on some condition, the value of the form control updates, but not the UI.

The UI changes however if you remove the input and manually set a value inside valueChanges.

### Reproduction

StackBlitz link: https://stackblitz.com/edit/qpu5ns
Steps to reproduce (1):
(1*. Select any date - optional)
1. Select the 10th of any month
2. Check date displayed in input vs date printed under the input

### Expected Behavior

We have the same date in the input as printed below the input

### Actual Behavior

The date in the input is the date selected using the datepicker, the date below the input is the date set inside valueChanges

### Environment

Browser: Chrome
(From the stackblitz environment)
Angular CLI: 16.1.0
Node: 18.18.0
Package Manager: yarn 1.22.19
OS: linux x64

Angular: 16.1.1
... animations, common, compiler, compiler-cli, core, forms
... platform-browser, platform-browser-dynamic, router

| Package | Version |
|--------|--------|
| @angular-devkit/architect | 0.1601.0 |
| @angular-devkit/build-angular | 16.1.0 |
| @angular-devkit/core | 16.1.0 |
| @angular-devkit/schematics | 16.1.0 |
| @angular/cdk | 16.2.9 |
| @angular/cli | 16.1.0 |
| @angular/material | 16.2.9 |
| @angular/material-moment-adapter | 16.2.9 |
| @schematics/angular | 16.1.0 |
| rxjs | 7.4.0 |
| typescript | 5.0.3 |

リンクされた StackBlitz の再現手順から始め、Angular Material components repository で reactive-forms による datepicker の値の更新経路を追跡します。valueChanges 内で値を設定した場合の動作を確認し、input UI が更新された form-control の値と一致することを示すリグレッションテストを追加します。

索引モデルが issue の本文から書いたものです。