Gemini Android app times out when AdGuard is enabled

### Please answer the following questions for yourself before submitting an issue

- [x] Filters were updated before reproducing an issue
- [x] I checked the [knowledge base](https://adguard.com/kb/) and found no answer
- [x] I checked to make sure that this issue has not already been filed

### AdGuard version

4.12.2

### Browser version

_No response_

### OS version

Android 16

### Issue Details

When AdGuard is running on Android, the Gemini app consistently fails to load responses and eventually times out. The issue only affects the Android Gemini app and does not occur when using Gemini via a browser or extension on desktop systems.

The same account and network work correctly:
in Firefox with the Gemini extension on Manjaro Linux
when AdGuard is disabled on Android

This suggests the issue is specific to the interaction between AdGuard for Android and the Gemini Android app.

Steps to Reproduce

1. Install the Gemini app on an Android device.
2. Enable AdGuard protection (VPN mode / default configuration).
3. Open the Gemini app.
4. Try to send a prompt or load a response.

### Expected Behavior

Gemini loads responses normally while AdGuard is enabled, just as it does when AdGuard is disabled or when using Gemini on desktop platforms.

### Actual Behavior

Gemini fails to load responses and eventually shows a timeout error only when AdGuard is running. Disabling AdGuard immediately resolves the issue.

### Screenshots

### Additional Information

_No response_