An assignment-triggered run that carried a handoff note showed the
generic "Initial run" label. Surface the note inline (truncated, like
comment triggers show their text) so the row reads as the handoff.
taskToResponse now populates handoff_note for all callers (dropping the
now-redundant explicit set in ClaimTaskByRuntime); the field is added to
the AgentTask type + zod schema (optional, additive — old clients ignore
it via the loose schema, new clients fall back to "Initial run").
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>