Fix cancellation, heartbeat, and LSP symbol budget issues

[Widthdom]

Summary

• Route LSP, MCP, and suggestion-store cancellation through the active request/shutdown tokens where issue reports found missing cancellation behavior.
• Observe JSON heartbeat and HTTP MCP handler background work, while preserving expected cancellation and handler semaphore cleanup.
• Cap and budget LSP document-symbol materialization/serialization, including pretty JSON response budgets.

Issue Scope

• No existing work-start comments were found on the requested issues before work began; work-start comments were posted for all five issues.
• No AGENTS.md, CLAUDE.md, or AGENT_GUIDE.md changes are included in this PR diff.

Validation

• dotnet run --project tools/CodeIndex.Changelog -- check
• git diff --check origin/main...HEAD
• dotnet build -p:UseSharedCompilation=false
• targeted issue tests for Thread cancellation through LSP, MCP status, and suggestion submission paths #3658, Standardize background heartbeat task observation and diagnostics #3705, Avoid repeated full JSON serialization while trimming LSP document symbols #3743, Cap LSP document symbol materialization before sorting #3758, Let BackgroundTaskObserver observe shutdown cancellation #3760
• dotnet test -p:UseSharedCompilation=false
• dotnet ./src/CodeIndex/bin/Debug/net8.0/cdidx.dll index . --json
• dotnet ./src/CodeIndex/bin/Debug/net8.0/cdidx.dll status --check --json
• adversarial review: no blocking/actionable issues found

Fixes #3658
Fixes #3705
Fixes #3743
Fixes #3758
Fixes #3760