Stabilize HOME shorthand log-path test

[Widthdom]

Summary

• isolate global-tool-log home-shorthand expansion assertions from filesystem writability fallback
• keep production log-directory resolution's writable-candidate requirement unchanged
• document the sandbox-safe test contract in both English and Japanese

Validation

• dotnet build
• dotnet test tests/CodeIndex.Tests/CodeIndex.Tests.csproj --no-restore --no-build --filter "FullyQualifiedName~ProgramRunnerTests.GlobalToolLog_OverrideDirectory_ExpandsHomeShorthand|FullyQualifiedName~ProgramRunnerTests.RunInstallerProcess_CancelsHungInstaller" --logger "console;verbosity=minimal" (net8.0 and net9.0; 8 passed)
• dotnet test tests/CodeIndex.Tests/CodeIndex.Tests.csproj --no-restore --no-build -f net8.0 --filter "FullyQualifiedName~ProgramRunnerTests" --logger "console;verbosity=minimal" (327 passed)
• dotnet run --project tools/CodeIndex.Changelog -- check (50 fragments validated)
• dotnet ./src/CodeIndex/bin/Debug/net8.0/cdidx.dll status --check --json
• Codex adversarial review: initial writability-fallback finding addressed; second round found no actionable regressions

Documentation and changelog

• updated TESTING_GUIDE.md in English and Japanese
• added changelog.d/unreleased/4810.fixed.md
• did not modify CHANGELOG.md

Follow-up candidates

• None.

Fixes #4810