Fix verbose JSON index output

[Widthdom]

Summary

• Route index --verbose --json status lines to stderr instead of suppressing them or writing them to stdout.
• Keep stdout as a parseable JSON-only stream for machine consumers.
• Add a regression test for update-mode --verbose --json stream separation.

Validation

• dotnet test tests/CodeIndex.Tests/CodeIndex.Tests.csproj --filter "FullyQualifiedName~IndexCommandRunnerTests.Run_UpdateMode_VerboseJson_WritesStatusToStderrAndKeepsStdoutJson"
• dotnet test tests/CodeIndex.Tests/CodeIndex.Tests.csproj --filter "FullyQualifiedName~IndexCommandRunnerTests"
• dotnet run --project tools/CodeIndex.Changelog -- check
• dotnet build CodeIndex.sln -c Release -p:UseSharedCompilation=false
• CLI smoke with a temporary project confirmed JSON stdout and verbose stderr separation.
• dotnet ./src/CodeIndex/bin/Debug/net8.0/cdidx.dll status --check --json

Documentation / Changelog

• Added changelog.d/unreleased/1471.fixed.md.

Review

• Attempted Codex adversarial review after rebasing scope onto current origin/main, but codex exec was blocked by account usage limit. Earlier Codex review ran before origin/main was refreshed and inspected unrelated diff, so it is not counted as a valid review for this final diff.

Fixes #1471