fix(client): detect Amp extension clients via amp.mcpServers key

[syf2211]

Summary

Fix false-positive "installed" status for Amp editor extensions (amp-vscode, amp-cursor, amp-windsurf, amp-vscode-insider) in thv client status.

Motivation

These Amp clients share the host editor's config directory (Code/User, Cursor/User, Windsurf/User). Checking only for directory presence reports Amp as installed whenever VS Code, Cursor, or Windsurf is installed, even without the Amp extension.

Fixes #2174

Changes

• Add optional InstallSettingsKey to clientAppConfig
• Set InstallSettingsKey: "amp.mcpServers" for Amp extension clients (not amp-cli, which has its own directory)
• Update IsClientInstalled to require the settings key when configured, using hujson + gjson with dot escaping for dotted JSON keys
• Add regression tests for Amp-on-Cursor detection

Tests

go test ./pkg/client/... -count=1

All tests pass.

Notes

• amp-cli is unchanged (dedicated ~/.config/amp directory)
• Uses the same JSONC parsing path as other client config readers
• A stale amp.mcpServers: null key after uninstall could still report installed; acceptable edge case per maintainer guidance

[codecov]

Codecov Report

❌ Patch coverage is 89.47368% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 70.35%. Comparing base (87bcb74) to head (38db8d4).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
pkg/client/discovery.go	89.47%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #5659      +/-   ##
==========================================
+ Coverage   70.33%   70.35%   +0.01%     
==========================================
  Files         649      651       +2     
  Lines       66185    66304     +119     
==========================================
+ Hits        46554    46647      +93     
- Misses      16277    16295      +18     
- Partials     3354     3362       +8     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.