[PM-42203] Add feature flag enable-basic-auth-response

[jprusik]

🎟️ Tracking

PM-42203

📔 Objective

Add feature flag enable-basic-auth-response

See corresponding clients work at bitwarden/clients#22612

[github-actions]

🤖 Bitwarden Claude Code Review

Overall Assessment: APPROVE

This PR adds a single feature flag constant, EnableBasicAuthResponse (enable-basic-auth-response), to the Autofill Team section of src/Core/Constants.cs. The constant name, kebab-case value, and placement match neighboring flags such as EnableAutofillTriage and LitInlineMenuComponents, and the key is unique across the repository. The flag is not yet referenced by server code, which is consistent with the linked clients-side work described in the PR body. No security, correctness, performance, or breaking-change concerns were identified.

Code Review Details

No findings.

[jprusik]

Test failures are pre-existing / from main (not introduced by these changes)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 63.19%. Comparing base (da39ab7) to head (58eb10d).

Additional details and impacted files

@@            Coverage Diff            @@
##           main    #8248       +/-   ##
=========================================
+ Coverage      0   63.19%   +63.19%     
=========================================
  Files         0     2409     +2409     
  Lines         0   104393   +104393     
  Branches      0     9453     +9453     
=========================================
+ Hits          0    65973    +65973     
- Misses        0    36162    +36162     
- Partials      0     2258     +2258     

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