Repository: flutter
Issue: Unable to add a Flutter module to a new Android app by following official documentation with `Depend on the module’s source code` option
Labels: platform-android,t: gradle,a: existing-apps,has reproducible steps,P2,team-android,triaged-android,found in release: 3.16,found in release: 3.19

### Steps to reproduce

I'm trying to integrate a flutter module to a newly created android app with the [documentation](https://docs.flutter.dev/add-to-app/android/project-setup?tab=with-android-studio) but i'm unable to resolve flutter dependencies with gradle....

1. Create app with latest AS (2023.1.1)
2. Integrate a new flutter module without AS (follow doc)
3. Do a gradle sync


**Workaround found :**

After hours, I removed this line from `settings.gradle` :

~~repositoriesMode.set(RepositoriesMode.PREFER_SETTINGS)~~

```
dependencyResolutionManagement {
  repositories {
    google()
    mavenCentral()
  }
}
```

which remove resolve warning from gradle. 

Is the documentation outdated ? 

### Actual results

With a gradle sync

![image](https://github.com/flutter/flutter/assets/1449422/79ec3c1a-e948-4849-b54f-86629ed67c1e)

### Logs

<details open>
<summary>Logs</summary>

```console
> Configure project :flutter
Build was configured to prefer settings repositories over project repositories but repository 'maven' was added by plugin class 'FlutterPlugin'
Build was configured to prefer settings repositories over project repositories but repository 'maven' was added by script '/home/william/Documents/flutter/packages/flutter_tools/gradle/module_plugin_loader.gradle'

> Task :prepareKotlinBuildScriptModel UP-TO-DATE

Deprecated Gradle features were used in this build, making it incompatible with Gradle 9.0.

You can use '--warning-mode all' to show the individual deprecation warnings and determine if they come from your own scripts or plugins.

For more on this, please refer to https://docs.gradle.org/8.2/userguide/command_line_interface.html#sec:command_line_warnings in the Gradle documentation.

BUILD SUCCESSFUL in 4s
```

</details>


### Flutter Doctor output

<details open>
<summary>Doctor output</summary>

```console

[✓] Flutter (Channel stable, 3.16.8, on Fedora Linux 39 (Workstation Edition) 6.6.12-200.fc39.x86_64, locale fr_FR.UTF-8)
    • Flutter version 3.16.8 on channel stable at /home/william/Documents/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 67457e669f (il y a 9 jours), 2024-01-16 16:22:29 -0800
    • Engine revision 6e2ea58a5c
    • Dart version 3.2.5
    • DevTools version 2.28.5

[✓] Android toolchain - develop for Android devices (Android SDK version 34.0.0)
    • Android SDK at /home/william/Android/Sdk
    • Platform android-34, build-tools 34.0.0
    • Java binary at: /home/william/.local/share/JetBrains/Toolbox/apps/android-studio/jbr/bin/java
    • Java version OpenJDK Runtime Environment (build 17.0.7+0-17.0.7b1000.6-10550314)
    • All Android licenses accepted.

[✓] Chrome - develop for the web
    • Chrome at google-chrome

[✓] Linux toolchain - develop for Linux desktop
    • clang version 17.0.6 (Fedora 17.0.6-1.fc39)
    • cmake version 3.27.7
    • ninja version 1.11.1
    • pkg-config version 1.9.5

[✓] Android Studio (version 2023.1)
    • Android Studio at /home/william/.local/share/JetBrains/Toolbox/apps/android-studio
    • Flutter plugin version 77.1.2
    • Dart plugin version 222.4582
    • Java version OpenJDK Runtime Environment (build 17.0.7+0-17.0.7b1000.6-10550314)

[✓] IntelliJ IDEA Community Edition (version 2023.3)
    • IntelliJ at /home/william/.local/share/JetBrains/Toolbox/apps/intellij-idea-community-edition
    • Flutter plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/6351-dart

[✓] VS Code (version 1.85.2)
    • VS Code at /usr/share/code
    • Flutter extension version 3.80.0

[✓] Connected device (3 available)
    • sdk gphone64 x86 64 (mobile) • emulator-5554 • android-x64    • Android 14 (API 34) (emulator)
    • Linux (desktop)              • linux         • linux-x64      • Fedora Linux 39 (Workstation Edition) 6.6.12-200.fc39.x86_64
    • Chrome (web)                 • chrome        • web-javascript • Google Chrome 120.0.6099.224

[✓] Network resources
    • All expected network resources are available.

• No issues found!


```

</details>