Inspector shows "Disconnected" after system sleep with no reconnect option, unlike Network tab which has offline/reconnect support

## Description
When the host machine goes to sleep while a Flutter debug session is running,
the DevTools Inspector panel becomes permanently disconnected and shows
"Run a new debug session to reconnect." — requiring a full app restart.

In contrast, the **Network tab** handles this gracefully:
- Shows the same "Disconnected" state
- Offers a **"Review recent data (offline)"** button
- Reconnects automatically or with a simple tab close/reopen

## Steps to Reproduce
1. Start a Flutter debug session
2. Open DevTools → Inspector
3. Let the machine go to sleep (or manually suspend)
4. Wake the machine
5. Observe Inspector is stuck in "Disconnected" state

## Expected Behavior
Inspector should either:
- **Option A:** Auto-reconnect when the VM Service becomes available again
- **Option B:** Show a "Reconnect" or "Refresh" button (similar to how
Network tab handles disconnection)

## Actual Behavior
Inspector shows "Disconnected - Run a new debug session to reconnect."
No reconnect/refresh option is available. A full app restart is required.

## Workaround
For Network tab: close and reopen the tab in DevTools → reconnects fine
For Inspector: must stop and re-run the entire debug session

## Proposal
Add a **Reconnect / Refresh button** to the Inspector's disconnected state,
consistent with the Network tab's offline handling UX.

## Environment
[✓] Flutter (Channel stable, 3.41.4, on macOS 26.3 25D125 darwin-arm64, locale en-UZ)
[✓] Android toolchain - develop for Android devices (Android SDK version 36.1.0)
[✓] Xcode - develop for iOS and macOS (Xcode 26.3)
[✓] Chrome - develop for the web
[✓] Connected device (3 available)
! Error: Browsing on the local area network for I.S.K.A.N.D.A.R. Ensure the device is unlocked and
attached with a cable or associated with the same local area network as this Mac.
The device must be opted into Developer Mode to connect wirelessly. (code -27)
[✓] Network resources

• No issues found!

Commencez par reproduire la séquence de mise en veille et de réveil avec une session de débogage Flutter, puis comparez l’état déconnecté de l’Inspector avec le comportement hors ligne et de reconnexion de l’onglet Network. Suivez le point d’entrée de l’état déconnecté de l’Inspector et déterminez comment la disponibilité de VM Service est détectée ; le travail est terminé lorsque l’Inspector peut se reconnecter ou propose une action reconnect ou refresh fonctionnelle sans redémarrer l’application.

Rédigé par le modèle d'indexation à partir du texte de l'issue.