Function apply_task_update 

pub fn apply_task_update(
    task: &mut SessionTask,
    update: SessionTaskUpdate,
    now: DateTime<Utc>,
)

Apply a partial update to a task, enforcing lifecycle invariants.

All registry backends route updates through this function so semantics stay identical across PostgreSQL, in-memory, and gRPC modes:

• terminal states are final: state changes on a terminal task are ignored (content fields like summary/result still apply);
• first transition out of queued stamps started_at;
• transition into a terminal state stamps finished_at;
• setting input_request forces awaiting_input; leaving awaiting_input clears it.