Constant CAPTCHA issues and failed payments when Tracking Protection 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

7.22.6

### Browser version

Chrome 147.0.7727.56

### OS version

Windows 11, 25H2 (OS Build 26200.7171)

### Traffic filtering

- [x] yes, I do

### Ad Blocking

AdGuard Base 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

None

### Language-specific

ROList

### Which DNS server do you use?

DNS protection disabled

### DNS protocol

DNS-over-HTTPS

### Custom DNS

Cloudflare DNS, managed by Windows.
1.1.1.1
1.0.0.1

### What Stealth Mode options do you have enabled?

Block trackers, Remove tracking parameters, Hide your search queries, Send Do-Not-Track header, Block WebRTC, Block Push API, Disable Windows Telemetry, Disable Windows Recall, Turn off Advertising ID, Disable Microsoft Defender automatic samples submission, Disable WAP Push Message Routing Service, Remove X-client-Data header from HTTP request, Protect from DPI

### Support ticket ID

_No response_

### Issue Details

I have been having a lot of issues lately with CAPTCHAs (sometimes endless loops of them), and with failed payments.
Basically, the internet has become unusable. If a website has a CAPTCHA, there is a very high chance AdGuard will trigger it (and fail the automated checks), regardless of the provider. (Google, Cloudflare, Alibaba, hCaptcha, etc.)
Even worse, many payments fail unless I disable AdGuard.
I can't even log in to my own Cloudflare account.

I narrowed the issue down to the "Tracking protection" feature from AdGuard.
Changing individual settings from this section has no effect. I even tested with all options disabled, and the problem persists. As long as the toggle to enable "Tracking protection" is ON, I have constant issues.
The problem goes away only when I disable this section entirely.

If it helps narrow down the issue, I sometimes see "Browser integrity check failed."
I also tested the free AdGuard AdBlocker extension with all "Tracking protection" options enabled, and it doesn't cause issues. This is something specific to the Desktop app.

PS: I think the problems started after the last update (or the one before it), about a month ago.

### Expected Behavior

Browse the internet without issues.

### Actual Behavior

Constant CAPTCHA issues and failed payments.