[codex] Fix MCP contracts, sampling, recipes, and HTTP SSE

[Widthdom]

Summary

• Split MCP tool argument name/allow-list contracts into a focused partial class.
• Require explicit CDIDX_MCP_SAMPLING opt-in before suggest_improvement calls MCP sampling.
• Expose MCP search recipe discovery/execution and bounded configured recipe sources.
• Add HTTP MCP SSE stream headers, health diagnostics, and multi-stream progress coverage.

Validation

• dotnet build
• dotnet test tests/CodeIndex.Tests/CodeIndex.Tests.csproj --no-build --filter FullyQualifiedName~Mcp (net8.0/net9.0: 700 passed)
• dotnet run --project tools/CodeIndex.Changelog -- check
• dotnet ./src/CodeIndex/bin/Debug/net8.0/cdidx.dll index . --commits HEAD --json
• dotnet ./src/CodeIndex/bin/Debug/net8.0/cdidx.dll status --check --json
• Codex adversarial review: No blocking/actionable issues found.

A full dotnet test tests/CodeIndex.Tests/CodeIndex.Tests.csproj --no-build run was attempted during this work and failed only in CodeIndex.Tests.QueryCommandRunnerTests.RunPublishedTrimmedCli_SerializesQueryJsonAndErrorJson because the local environment lacks Microsoft.NETCore.App 10.0.8-servicing.26229.119; this is already tracked by #3571 and #3573.

Issues

Fixes #3382
Fixes #3405
Fixes #3545
Fixes #3522

Notes

AGENTS.md, CLAUDE.md, and AGENT_GUIDE.md were not modified.