Fix DbReader schema cache reuse for issue #1701

[Widthdom]

Summary

• Add a process-level DB-path keyed schema cache for DbReader schema discovery.
• Reuse cached table columns, index lists, and table-existence checks across DbContext instances while invalidating on SQLite schema_version changes.
• Document the schema cache contract and add a bilingual changelog fragment.

Fixes #1701

Documentation / Changelog

• Updated DEVELOPER_GUIDE.md.
• Added changelog.d/unreleased/1701.fixed.md.

Validation

• dotnet build
• dotnet test tests/CodeIndex.Tests/CodeIndex.Tests.csproj --filter "FullyQualifiedName~DbSchemaCacheTests"
• dotnet run --project tools/CodeIndex.Changelog -- check
• dotnet test
• dotnet ./src/CodeIndex/bin/Debug/net8.0/cdidx.dll status --check --json

Review

• Adversarial review: No blocking/actionable issues found.

Follow-up candidates

• None.