[investigate] Browsing session from incognito window sometimes leaks to normal window when "delete third-party cookies" option 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 Extension version

5.4.3.1

### Browser version

Firefox 151.0.3

### OS version

Windows 11

### Ad Blocking

AdGuard Base filter

### Privacy

AdGuard Tracking Protection filter, AdGuard URL Tracking filter

### Social

AdGuard Social Media filter

### Annoyances

AdGuard Annoyances filter, AdGuard Cookie Notices filter, AdGuard Popups filter, AdGuard Other Annoyances filter, AdGuard Widgets filter, Fanboy's Annoyances

### Security

Online Malicious URL Blocklist, Phishing URL Blocklist, uBlock Origin – Badware risks

### Other

_No response_

### Language-specific

Dandelion Sprout's Serbo-Croatian List

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

Block trackers, Remove tracking parameters, Hide your search queries, Ask websites not to track you, Self-destruction of third-party cookies, Hide Referrer from third parties

### Issue Details

Steps to reproduce:
1. Open [youtube.com](https://youtube.com/) in normal window
2. Enable `delete third-party cookies` under `tracking protection` in extension settings
3. Open incognito window, visit [youtube.com](https://youtube.com/) and sign-in
4. Once signed-in, refresh [youtube.com](https://youtube.com/) opened in normal window

### Expected Behavior

Shouldn't be signed into YouTube account in normal window, only incognito window.

### Actual Behavior

Signed in normal window and incognito window.

### Screenshots

Video

https://github.com/user-attachments/assets/bff14e58-d503-4588-b52e-64254763a36d

### Additional Information

I was searching if someone reported this before, but couldn't find anything.