Rename BackgroundTask and attempt ID fields to camelCase across background-agent consumers while moving BackgroundManager construction to a single config object.
Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)
Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>
Match opencode core 'task' tool behavior for metadata consistency:
1. Model fallback: When categoryModel/task.model/resumeModel is undefined,
fall back to parentContext.model so subagent metadata always includes
model info. Thread parentContext into executeSyncContinuation for parity.
2. Task ID consistency: unstable-agent-task was missing taskId and
backgroundTaskId in metadata. background_output used inconsistent
snake_case 'task_id' vs camelCase 'taskId' elsewhere. Standardize on
camelCase: taskId = sessionID (resume id), backgroundTaskId = bg task id.
Update text output blocks to use buildTaskMetadataBlock helper.
Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)
Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>
YeonGyu-Kim