Running web app from Android Studio is not preserving the last build session

Launch Config for VS Code:
```
{
"name": "Flutter-web",
"request": "launch",
"type": "dart",
"program": "lib/main.dart",
"args": [
"-d",
"chrome",
"--web-port",
"55586",
"--web-browser-flag=--disable-web-security"
]
},
```

Launch Config for Android Studio:
```





```

## Issue Description

When running my Flutter web app from VS Code on port 55586, the app resumes from where I left off after being killed and re-run. It preserves all user data, session tokens, and other information unless flutter clean is executed.

However, when running the same app from Android Studio on port 55587, the app creates a fresh instance every time it is killed and re-run. Despite using the same port, user sessions, tokens, and other information are erased.

## Version info

• Flutter version 3.22.2
• Dart version 3.4.3
• DevTools version 2.34.3
• Android Studio (version 2024.1)
• Flutter IntelliJ plugin version 80.0.2

## Expected Behavior

The Flutter web app should preserve the user session, tokens, and other information between runs when using Android Studio, similar to the behavior in VS Code.

The report provides lib/main.dart and launch configurations for VS Code and Android Studio. First reproduce the two runs with the supplied ports and compare how each launch path handles a killed and restarted app. Done means the Android Studio launch preserves the user session and stored data in the same way as the VS Code launch.

Written by the indexing model from the issue text.