feat(settings): add search bar to settings modal

[TharunikaaM]

Summary

This PR adds a search bar to the Settings modal, making it easier to quickly locate settings without manually scrolling through the sidebar.

Before

Users had to manually browse through different sections to find a specific setting.

After

A search bar is available at the top of the Settings sidebar, allowing users to filter settings live as they type.

Search bar

Searching for a setting

Changes

• Added a search bar to the top of the Settings sidebar.
• Filters settings dynamically as the user types.
• Supports case-insensitive search.
• Searches across both settings and section names.
• Displays a "No settings found" message when there are no matching results.
• Clears the search query when the Settings modal is closed.

Testing

Tested the following scenarios:

• Live filtering while typing
• Case-insensitive search
• Section and setting name matching
• "No settings found" state
• Search reset when closing the Settings modal

Fixes #1672

[mergify]

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[greptile-apps]

Confidence Score: 5/5

This looks safe to merge.

• No blocking issues found in the changed code.

Important Files Changed

Filename	Overview
frontend/src/components/Settings/Settings.vue	Adds sidebar search and keeps the selected settings page aligned with filtered and empty states.

_{Reviews (2): Last reviewed commit: "Merge remote-tracking branch 'upstream/d..." | Re-trigger Greptile}

[mergify]

@TharunikaaM this pull request has merge conflicts. Please resolve them so it can be reviewed and merged.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 60.53%. Comparing base (7c22813) to head (d898833).
⚠️ Report is 227 commits behind head on develop.

Additional details and impacted files

@@           Coverage Diff            @@
##           develop    #2377   +/-   ##
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  Coverage    60.53%   60.53%           
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  Files          142      142           
  Lines         8550     8550           
========================================
  Hits          5176     5176           
  Misses        3374     3374           

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