## Why
Full WebSocket requests previously used the generic `other` reason when continuation failed because request properties or input changed, obscuring why incremental reuse was unavailable.
## What changed
- Report specific reasons for changed request properties, shortened or mismatched input, and missing response state or response IDs.
- Add `previous_item_type` and `current_item_type` labels to continuation metrics and failure traces. Diagnostics use bounded labels without request contents or identifiers.
- Centralize response item type names in `ResponseItem::item_type()` and reuse them for output logging.
## Testing
Add coverage for unavailable response state and empty response IDs. Expand WebSocket tests to check fallback reasons and item types for rewritten or shortened input, replaced input, changed model, and changed output schema, including precedence when multiple properties change.
GitOrigin-RevId: 3951853dfe87d40b7046af6f6a8efd5d4f5b06d1