'Hide Referer from third parties' breaks some websites and unblocking rules are not working in Firefox

### 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 Extension version

4.4.22

### Browser version

Firefox 131

### OS version

Windows 11

### Ad Blocking

AdGuard Base filter

### Privacy

_No response_

### Social

_No response_

### Annoyances

_No response_

### Security

_No response_

### Other

_No response_

### Language-specific

_No response_

### What Tracking protection options do you have enabled?

Hide Referrer from third parties

### Issue Details

Steps to reproduce:
1. Enable 'Hide Referer from third parties'
2. Go to https://yandex.ru/search/?text=%D1%8F&from=os&lr=10741&ncrnd=382 and click on the profile button

Screenshot


3. Go to User rules and add `@@yandex.*/user-id?$stealth=referrer|searchqueries`
4. Check the popup content from step 2

### Expected Behavior

_No response_

### Actual Behavior

popup content is missing

Screenshot


### Screenshots

_No response_

### Additional Information

_No response_