Too long determining workmode

### 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

Every time the app is opened, there is a lengthy ‘determining workmode’ process in the new version 4.1.1, even in non-root mode. I used non-root mode because I’d previously experienced the same issue with other modes taking a long time to load, and having to wait for it to prompt for pairing or connect via wireless debugging.

### To Reproduce

_No response_

### Expected behavior

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### Screenshots

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### Logs

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### Device info

- Device: Redmi Note 9 Pro
- OS Version: Android 12, MIUI 14
- App Manager Version: 4.0.1
- Mode: Root/ADB/NonRoot

### Additional context

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Start by reproducing the lengthy “determining workmode” process when opening App Manager on the reported Android 12 device, checking both non-root and other modes. Compare the behavior with the reported App Manager versions and collect the logs requested by the issue template; done means startup workmode detection no longer takes an excessive time or its cause is identified.

Written by the indexing model from the issue text.