Repository: flutter
Issue: Why are there no libraries (pods) in iOS target (extension)?
Labels: platform-ios,P3,team-ios,triaged-ios

### Steps to reproduce

1) I am adding a new target - AutoFill Credential Provider:

<img width="500" alt="Снимок экрана 2024-01-24 в 16 44 40" src="https://github.com/flutter/flutter/assets/121060849/a9f03f58-e994-41c2-a73c-fbe60fd27eeb">

2) I do everything as written here - https://docs.flutter.dev/platform-integration/ios/app-extensions
3) In the settings "passwords" in the simulator choose my application:

<img height="600" alt="Снимок экрана 2024-01-24 в 17 01 05" src="https://github.com/flutter/flutter/assets/121060849/137bb579-2ef3-43f6-8d9e-d5d587703178">

4) on some site I try to enter a password and click on "passwords":

<img height="600" alt="Снимок экрана 2024-01-24 в 17 02 17" src="https://github.com/flutter/flutter/assets/121060849/fa70343e-b6f8-4572-a649-fdf5f9785654">



### Expected results

I expect that when I open the app through the "passwords" then I will see my app fully working, but only through extension. For example a simple screen with login:

<img height="600" alt="Снимок экрана 2024-01-24 в 16 49 50" src="https://github.com/flutter/flutter/assets/121060849/16ad2a8b-6049-4e97-9a9d-385179271b02">


### Actual results

But I get it wrong. I use Firebase, and so I understand that this extension (target) does not see my packages that I added to pubspec.yaml, or does not see pods pods: 

<img height="600" alt="Снимок экрана 2024-01-24 в 16 53 13" src="https://github.com/flutter/flutter/assets/121060849/1d833654-8adc-4367-b6c1-8782a2b0a168">


### Code sample

Example of how to open flutter in swift code

<details open><summary>CredentialProviderViewController.swift</summary>

```swift
import AuthenticationServices
import Flutter
import UIKit

class CredentialProviderViewController: ASCredentialProviderViewController  {
    override func prepareCredentialList(for serviceIdentifiers: [ASCredentialServiceIdentifier]) {
        showFlutter()
    }
    
    
    @IBAction func cancel() {
        self.extensionContext.cancelRequest(withError: NSError(domain: ASExtensionErrorDomain, code: ASExtensionError.userCanceled.rawValue))
    }

    func showFlutter() {
        let flutterViewController = FlutterViewController(project: nil, nibName: nil, bundle: nil)
        addChild(flutterViewController)
        view.addSubview(flutterViewController.view)
        flutterViewController.view.frame = view.bounds
    }
}


```

</details>


### Screenshots or Video

<details open>
<summary>Screenshots / Video demonstration</summary>

[Upload media here]

</details>


### Logs

<details open><summary>Logs</summary>

```console
[Paste your logs here]
```

</details>


### Flutter Doctor output

<details open><summary>Doctor output</summary>

```console
[✓] Flutter (Channel stable, 3.16.8, on macOS 14.2.1 23C71 darwin-arm64, locale ru-RU)
    • Flutter version 3.16.8 on channel stable at /Users/skripov/Documents/dev/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 67457e669f (8 days ago), 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 /Users/skripov/Library/Android/sdk
    • Platform android-34, build-tools 34.0.0
    • Java binary at: /Applications/Android Studio.app/Contents/jbr/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build 17.0.7+0-17.0.7b1000.6-10550314)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 15.2)
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • Build 15C500b
    • CocoaPods version 1.14.3

[✓] Chrome - develop for the web
    • Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2023.1)
    • Android Studio at /Applications/Android Studio.app/Contents
    • 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
    • Java version OpenJDK Runtime Environment (build 17.0.7+0-17.0.7b1000.6-10550314)

[✓] VS Code (version 1.85.2)
    • VS Code at /Users/skripov/Documents/dev/Visual Studio Code.app/Contents
    • Flutter extension version 3.80.0

[✓] Connected device (4 available)
    • iPhone (Александр) (3) (mobile) • 00008110-000825240E9A401E            • ios            • iOS 17.2.1 21C66
    • iPhone 13 (mobile)              • 089E096C-387A-4817-86B8-CD9DB8C30415 • ios            •
      com.apple.CoreSimulator.SimRuntime.iOS-17-2 (simulator)
    • macOS (desktop)                 • macos                                • darwin-arm64   • macOS 14.2.1 23C71
      darwin-arm64
    • Chrome (web)                    • chrome                               • web-javascript • Google Chrome
      120.0.6099.234

[✓] Network resources
    • All expected network resources are available.

• No issues found!
```

</details>