[PM-39184] Clear clipboard setting does not clear clipboard

### Steps To Reproduce

1. Set clear clipboard to 10 seconds
2. Copy a password from a vault item
3. Wait 10 seconds

### Expected Result

Clipboard is cleared

### Actual Result

Clipboard is not cleared

### Screenshots or Videos

_No response_

### Additional Context

_No response_

### Build Version

2026.6.1 (21675)

### What server are you connecting to?

US

### Self-host Server Version

_No response_

### Environment Details

- Device: Samsung Galaxy S25+
- Android 16

### Issue Tracking Info

- [x] I understand that work is tracked outside of Github. A PR will be linked to this issue should one be opened to address it, but Bitwarden doesn't use fields like "assigned", "milestone", or "project" to track progress.

No source file or test is named. Reproduce the failure on a Samsung Galaxy S25+ running Android 16 with the clear-clipboard setting set to 10 seconds, then trace the Android clipboard-clearing path from copying a vault password. Done means the clipboard is cleared after the configured delay and the behavior is covered by a regression test.

Written by the indexing model from the issue text.