[PM-16932] Fix timeout when desktop app is not started

[quexten]

🎟️ Tracking

https://bitwarden.atlassian.net/browse/PM-16932

📔 Objective

Prevents a 5 second wait period, that is needed for the legacy biometrics protocol. Since the status is re-checked every second, timing out means it will temporarily be unavailable, and if the desktop app starts later, it will be enabled again.

📸 Screenshots

⏰ Reminders before review

• Contributor guidelines followed
• All formatters and local linters executed and passed
• Written new unit and / or integration tests where applicable
• Protected functional changes with optionality (feature flags)
• Used internationalization (i18n) for all UI strings
• CI builds passed
• Communicated to DevOps any deployment requirements
• Updated any necessary documentation (Confluence, contributing docs) or informed the documentation team

🦮 Reviewer guidelines

• 👍 (:+1:) or similar for great changes
• 📝 (:memo:) or ℹ️ (:information_source:) for notes or general info
• ❓ (:question:) for questions
• 🤔 (:thinking:) or 💭 (:thought_balloon:) for more open inquiry that's not quite a confirmed issue and could potentially benefit from discussion
• 🎨 (:art:) for suggestions / improvements
• ❌ (:x:) or ⚠️ (:warning:) for more significant problems or concerns needing attention
• 🌱 (:seedling:) or ♻️ (:recycle:) for future improvements or indications of technical debt
• ⛏ (:pick:) for minor or nitpick changes

[github-actions]

Checkmarx One – Scan Summary & Details – 4094712d-561a-40d3-b48a-80d15aef1012

No New Or Fixed Issues Found

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 34.14%. Comparing base (2439e23) to head (f1d93b6).

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@                        Coverage Diff                        @@
##           km/fix-biometrics-browser-prompt   #12799   +/-   ##
=================================================================
  Coverage                             34.14%   34.14%           
=================================================================
  Files                                  2937     2937           
  Lines                                 90419    90347   -72     
  Branches                              16988    16965   -23     
=================================================================
- Hits                                  30870    30850   -20     
+ Misses                                57090    57041   -49     
+ Partials                               2459     2456    -3     

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