Cannot log into twitch.tv when AdGuard Extra is enabled

### Prerequisites

- [x] Filters were updated before reproducing an issue
- [x] AdGuard Extra version is up-to-date
- [x] I checked to make sure that this issue has not already been filed

### What product do you use?

AdGuard Extra with other script manager

### What type of problem have you encountered?

AdGuard Extra gets detected on a website

### Which browser(s) do you use?

other (specify in comment below)

### Where is the problem encountered?

https://twitch.tv

### What filters do you have enabled?

---Third-party filters---

### Issue Details

Please refer to Additional Information for user-specific information in case relevant. I also list the filters used with my adblocker that I use in conjunction there.

Steps to reproduce:
1. Go to twitch.tv in a logged-out state (e.g. after clearing browser cache) with the AdGuard Extra extension enabled
2. Click the Log In button
3. Enter login information, and click the button to log in.
4. Receive error message "Your browser is not currently supported. Please use a recommended browser or learn more here."
5. Close the twitch.tv tab
7. Clear browser cache for twitch.tv
8. Follow steps 1-3 but with the AdGuard Extra extension disabled
9. No issues are encountered in logging in

### Expected Behavior

twitch.tv does not have different behavior when AdGuard Extra is enabled

### Actual Behavior

twitch.tv prohibits logging in with a confusing error message about the browser not being supported

### Screenshots

twitch.tv "browser not supported" error


### Additional Information

User-specific details:
- Browser: Brave 1.74.50 Chromium: 132.0.6834.111 (Official Build) (arm64)
- AdGuard Extra extension version: 1.0.658
- Operating system: macOS Sonoma 14.7.2
- Adblocker used in conjunction: uBlock Origin extension 1.62.0 with **default** filters (listed below for convenience):
- uBlock filters – Ads
- uBlock filters – Badware risks
- uBlock filters – Privacy
- uBlock filters – Quick fixes
- uBlock filters – Unbreak
- EasyList
- EasyPrivacy
- Online Malicious URL Blocklist
- Peter Lowe’s Ad and tracking server list
- Custom filters that are applied universally just in case relevant:
```css
##.ytp-pause-overlay
##.ytp-scroll-min
##.ytp-ce-shadow
##.ytp-ce-element

###hot-network-questions
##.sidebar-related.module
##.sidebar-linked.module
```
- Network/DNS: I use [Fabston's Malicious Blocklist](https://github.com/fabston/little-snitch-blocklist) with Little Snitch, which blocks the following domains that have twitch in the domain name:
- analytics.m7g.twitch.tv
- ads.twitch.tv
- fan.twitch.tv
- ad.twitchguru.com
- follower-twitch.fr
- pulse-twitch.ru
- railroadmanytwitch.com
- staunchgenetwitch.com
- strewtwitchlivelihood.com
- throwinterrogatetwitch.com
- twitch-drops.lol
- twitch-face-punch.ru
- twitch-facepunch.lol
- twitch-nude.com
- twitch-survival.online
- twitch-tv.top
- twitch.photos
- twitchindoor.best

### Privacy

- [x] I agree to follow this condition