App Manager ADB mode breaks Automate Shizuku connectivity after recent update

### Please check before submitting an issue

- [x] I know what my device, OS and App Manager versions are
- [x] I know how to take logs
- [x] I know that generating a report, in whole part or in part, using AI/LLM is prohibited
- [x] I know how to reproduce the issue which may not be specific to my device

### Describe the bug

This issue started immediately after updating App Manager to the latest version.
Before this update, the same setup worked reliably:
Automate could consistently connect to Shizuku
No ADB connectivity issues after reboot
However, after the update, Automate can no longer reliably connect to Shizuku after reboot when App Manager ADB mode is enabled.
Error log (Automate)
android.system.ErrnoException: isConnected failed: ECONNREFUSED (Connection refused)
Shizuku is unavailable via ADB on 172.30.1.11:xxxxx

### To Reproduce

Install Shizuku and enable wireless debugging
Install Automate and configure Shizuku Keeper flow
Enable App Manager ADB mode
Reboot device
Run Automate flow

### Expected behavior

Automate should connect to Shizuku normally after reboot, as it did before the App Manager update.
After the recent App Manager update, Automate fails to connect to Shizuku via ADB with ECONNREFUSED, and Shizuku is reported as unavailable on the wireless debugging endpoint.

### Screenshots

_No response_

### Logs

_No response_

### Device info

Android device (Samsung One UI)
Shizuku (wireless debugging / ADB mode)
Automate (Shizuku Keeper flow / ADB shell command blocks)
App Manager with ADB mode enablede:
- OS Version:
- App Manager Version:
- Mode: Root/ADB/NonRoot

### Additional context

Disabling App Manager ADB mode (switching it off or setting it to non-ADB behavior) immediately restores normal functionality between Automate and Shizuku.
This strongly suggests the issue is triggered specifically by App Manager’s ADB handling.

Start with the App Manager ADB mode and the reproduce sequence: enable wireless debugging, configure the Automate Shizuku Keeper flow, reboot, and run it. Collect the missing App Manager and OS versions plus logs, then compare ADB mode enabled with non-ADB behavior; done means Automate reconnects to Shizuku after reboot without ECONNREFUSED.

Written by the indexing model from the issue text.