[PM-17820] - Browser/Web - update button and label state in username generator

[jaasen-livefront]

🎟️ Tracking

https://bitwarden.atlassian.net/browse/PM-17820

📔 Objective

This PR adds the missing event handler for setting the button text and generated value in the username generator dialog for the web and browser.

📸 Screenshots

Screen.Recording.2025-01-31.at.11.16.12.AM.mov

Screen.Recording.2025-01-31.at.11.15.11.AM.mov

⏰ 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 – 18f898ff-01e1-4275-842a-21441275df8c

Great job, no security vulnerabilities found in this Pull Request

[codecov]

Codecov Report

Attention: Patch coverage is 50.00000% with 6 lines in your changes missing coverage. Please review.

Project coverage is 35.48%. Comparing base (ca53ecc) to head (cc81f45).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
...nerator-dialog/vault-generator-dialog.component.ts	50.00%	1 Missing and 2 partials ⚠️
...generator-dialog/web-generator-dialog.component.ts	50.00%	1 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #13189      +/-   ##
==========================================
- Coverage   35.48%   35.48%   -0.01%     
==========================================
  Files        3007     3007              
  Lines       90899    90901       +2     
  Branches    16908    16908              
==========================================
  Hits        32260    32260              
  Misses      56137    56137              
- Partials     2502     2504       +2     

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