<!-- This is an auto-generated comment: release notes by coderabbit.ai -->
## Summary by CodeRabbit
- **Bug Fixes**
- Improved handling of document statuses to ensure documents without a finished or existing status are now explicitly marked as "processing" instead of remaining undefined.
- **Tests**
- Added comprehensive new tests and snapshot entries to verify document status merging, including edge cases and concurrent operations, ensuring robust and consistent behavior.
- **Enhancements**
- Updated context document listings to display the processing status for relevant documents.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->