Structured (native chat) sessions have no PTY and no hook script, so their
status never reached the hook server's store; #19217 gave `worktree ps` its
own adapter over the structured feed instead. The feed now writes every
projection into that store through a status sink the runtime wires, drops
the row when the host closes the session, and `worktree ps` reads the one
snapshot like every other agent.
Rows carry a `structuredHost` marker and the journal clock; they are never
persisted to last-status.json, and the main process does not forward them
to the renderer yet, whose feed bridge still owns them until it is retired.
Design and the two follow-ups: docs/reference/agent-status-store.md.