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!

まず、Flutter のデバッグセッションでスリープと復帰のシーケンスを再現し、その後、Inspector の切断状態と Network タブのオフラインおよび再接続時の動作を比較します。Inspector の切断状態へのエントリポイントを追跡し、VM Service の利用可能性がどのように検出されるかを特定します。アプリを再起動せずに Inspector が再接続できるか、機能する reconnect または refresh アクションを提示できれば完了です。

索引モデルが issue の本文から書いたものです。