[investigate] Ads are not blocked when "Continue where you left off On startup"

### 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

5.3.0.29

### Browser version

Chrome 146.0.7680.165

### OS version

macOS 26.4 (25E246)

### Ad Blocking

AdGuard Base filter, AdGuard Mobile Ads filter

### Privacy

AdGuard Tracking Protection filter, AdGuard URL Tracking filter

### Social

AdGuard Social Media filter

### Annoyances

AdGuard Cookie Notices filter, AdGuard Popups filter, AdGuard Mobile App Banners filter, AdGuard Other Annoyances filter, AdGuard Widgets filter

### Security

Online Malicious URL Blocklist

### Other

_No response_

### Language-specific

_No response_

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

Block trackers, Remove tracking parameters, Hide your search queries, Ask websites not to track you, Remove X-Client-Data header, Disable WebRTC

### Issue Details

Steps to reproduce:
1. Select "Continue where you left off" in "On startup" in Chrome Settings.
2. Open a Youtube video.
3. Quit the browser.
4. Open the browser.

### Expected Behavior

Youtube video plays with no ads and user rules loads normally (like moving chat below video).

### Actual Behavior

Youtube video plays with ads and user rules does not load normally.

### Screenshots

### Additional Information

_No response_