[DevTools 2.48.0] Network Page stops capturing requests after Clear + Restart (works on 2.42.3)

On Flutter 3.35.4 (Dart 3.9.2, DevTools 2.48.0) the Network tab in Dart DevTools stops capturing any requests after using "Clear" and then doing "Restart" in debug mode.

On the same project with Flutter 3.29.3 (Dart 3.7.2, DevTools 2.42.3) everything works correctly.
So the regression appeared between DevTools 2.42.3 and 2.48.0.

Steps to reproduce:
1. Run Flutter app in debug mode (VS Code or Android Studio).
2. Open Dart DevTools → Network.
3. Do some network requests → they are captured correctly.
4. Press "Clear".
5. Restart the app from IDE.
6. No new requests are captured anymore.

Expected result:
Network page continues to capture requests after Clear + Restart.

Actual result:
Network page stays empty, no requests appear.

**Environment:**
Flutter 3.35.4 • Dart 3.9.2 • DevTools 2.48.0
OS: Windows 10
IDE: VS Code (latest)

**Works fine with:**
Flutter 3.29.3 • Dart 3.7.2 • DevTools 2.42.3