BrowserViewportService: Improve CancellationToken logic

[ScarletKuro]

Description

Fixes: #9985

I think this should completely resolve the problem.

Type of Changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Documentation (fix or improvement to the website or code docs)

Checklist

• The PR is submitted to the correct branch (dev).
• My code follows the code style of this project.
• I've added relevant tests.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 90.96%. Comparing base (28bc599) to head (b44011e).
Report is 571 commits behind head on dev.

Additional details and impacted files

@@            Coverage Diff             @@
##              dev   #10012      +/-   ##
==========================================
+ Coverage   89.82%   90.96%   +1.13%     
==========================================
  Files         412      409       -3     
  Lines       11878    12525     +647     
  Branches     2364     2446      +82     
==========================================
+ Hits        10670    11393     +723     
+ Misses        681      577     -104     
- Partials      527      555      +28     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.