csp rule with $domain does not work on the first page load from NTP

### 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

5.4.3.85

### Browser version

Chrome 150.0.7871.47

### OS version

Windows 11 Pro

### 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?

_No response_

### Issue Details

See https://github.com/AdguardTeam/AdguardFilters/issues/202431#issuecomment-4829240042 and Adam's reply. No such issue for the MV2 extension.

### Expected Behavior

`$csp,domain=` should work equally as `$csp,to=`

### Actual Behavior

Only `$csp,domain=` does not work, and only on the first load from new tab page.

### Screenshots

NA

### Additional Information

_No response_

No concrete files or tests are referenced in the issue. Start by tracing the extension code path that parses and applies `$csp` modifiers, then compare the behavior between `domain=` and `to=` variants. Next, inspect the New Tab Page first-load flow to identify why domain-scoped CSP may be skipped only on that path. Done means a fresh NTP load consistently applies `$csp,domain=` like `$csp,to=`, with tests or manual verification added to cover that case.

索引モデルが issue の本文から書いたものです。