Remove unused private helpers

[Widthdom]

Summary

• remove four declaration-only private members from the search, LSP, Markdown, and JavaScript/TypeScript extractor paths
• preserve existing behavior; no deletion-name-only tests were added
• record the internal cleanup in a bilingual changelog fragment without claiming an unmeasured performance improvement

Validation

• fresh local index checks for the root database and workspace manifest
• complete generated-inclusive find --all --count --json checks: each candidate had one declaration before the change and zero occurrences after it
• dotnet build CodeIndex.sln -c Release -p:UseSharedCompilation=false --warnaserror (0 warnings, 0 errors)
• targeted QueryCommandRunnerTests, LspServerTests, and SymbolExtractorTests on net8.0 (3,003 passed, 1 skipped) and net9.0 (2,939 passed, 65 skipped)
• full Release suite on net8.0 (12,326 passed, 9 skipped) and net9.0 (11,837 passed, 435 skipped)
• dotnet format CodeIndex.sln --verify-no-changes --no-restore
• dotnet run --project tools/CodeIndex.Changelog -- check
• an additional review-time Debug run reported two transient HTTP MCP temporary-directory cleanup failures; both tests passed when rerun in isolation on net9.0

Documentation and changelog

• added changelog.d/unreleased/5283.internal.md
• no user-facing documentation changed because this removes private, unreferenced implementation details without changing a public contract

Review

• Codex adversarial review of origin/main..HEAD: No blocking/actionable issues found.

Follow-up candidates

• None.

Fixes #5283