[PM-31497] use remove auth logic for remove password

[itsadrago]

🎟️ Tracking

https://bitwarden.atlassian.net/browse/PM-31497

📔 Objective

We need to convert the remove password endpoint to use logic from the remove auth endpoint. Right now, we have some redundant logic, and in addition, by using the remove auth logic we have more time to convert all clients to use the remove auth endpoint so that we can eventually decommission the remove password endpoint.

⏰ 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 – 13fab8e5-b464-4751-9e68-8c86411cb4fe

Great job! No new security vulnerabilities introduced in this pull request

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 56.06%. Comparing base (51aa419) to head (ac10335).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #6929      +/-   ##
==========================================
- Coverage   60.01%   56.06%   -3.95%     
==========================================
  Files        1971     1971              
  Lines       87090    87083       -7     
  Branches     7759     7757       -2     
==========================================
- Hits        52266    48827    -3439     
- Misses      32928    36450    +3522     
+ Partials     1896     1806      -90     

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