server-side TurnState in the harness, exposed via /api/state

new TurnState { Idle, Thinking, Compacting } on hive_ag3nt::events::Bus
with set_state + state_snapshot. the turn loops in hive-ag3nt and
hive-m1nd flip Thinking before drive_turn and Idle after; the
web_ui's /api/compact handler flips Compacting around compact_session.

per-agent /api/state grows turn_state + turn_state_since (unix
seconds). frontend prefers the server-reported state over the
client-derived one — setStateAbs takes the absolute since-time so
the 'last turn' chip reads the actual server-side duration instead
of the client's perceived gap between SSE events. SSE turn_start /
turn_end still drive state instantly between renders; /api/state
re-anchors on each turn_end refresh.

new compacting state gets its own purple badge with pulse
animation (mirrors thinking's amber). napping will slot in the
same way once the nap tool lands.

TODO.md

@@ -27,19 +27,10 @@ Pick anything from here when relevant. Cross-cutting design notes live in
 
 ## UI / UX
 
-- **State badge: compacting + napping states.** Idle/thinking already
-  ship (driven from SSE turn_start/turn_end). Add `compacting 📦` and
-  `napping 😴` once the `/compact` trigger and `nap` tool exist —
-  both need a harness signal (an explicit `LiveEvent::StateChange`
-  variant or piggyback on Note).
-- **Server-side state badge.** Today the badge is computed client-side
-  from `turn_start`/`turn_end` events. On page reload mid-turn the
-  history replay re-derives it, but with a `compacting` / `napping`
-  state coming and a non-trivial state machine it's better to track
-  authoritative state in the harness and expose it via
-  `GET /api/state` (`status: "thinking" | "idle" | "compacting" |
-  "napping"`). JS just renders. Drops the
-  derive-from-events-and-pray code path.
+- **State badge: napping state.** Idle / thinking / compacting
+  already ship from server-side `TurnState`. Add `napping 😴`
+  once the `nap` tool exists — it just adds a new `TurnState`
+  variant the harness flips into for the duration of the nap.
 - **Terminal: `/model` slash command.** Operator-typeable model
   override from the terminal. Depends on the model-override work
   above; once an override mechanism exists, wire a `/model <name>`