agent page: consolidate alive/thinking/paused into one status badge

mara, #3757: fold the separate alive badge into the turn-state badge,
with pause/resume + cancel-turn moved into its dropdown. Cancel-turn is
click-again-to-confirm, not a modal.

model/effort/ctx/cost stay as separate badges — not asked to fold
those in too.

frontend/packages/agent/src/Root.tsx

@@ -142,10 +142,8 @@ export function Root() {
       <>
         <Header label="…" pills={pills}>
           <StatusChips
-            aliveLabel="… connecting"
-            aliveTone="neutral"
-            stateLabel="… booting"
-            stateTone="neutral"
+            statusLabel="… connecting"
+            statusTone="neutral"
             model=""
             availableModels={[]}
             onSelectModel={() => {}}
@@ -175,6 +173,24 @@ export function Root() {
   const effectiveTurnState = state.status === 'online' ? state.turn_state : 'offline';
   const turnDef = STATE_LABELS[effectiveTurnState] ?? { glyph: '○', text: 'offline', tone: 'negative' as BadgeTone };
   const stateAge = fmtAge(Date.now() - state.turn_state_since * 1000);
+  // Consolidated status badge (mara: "why do we have separate alive
+  // badge? ... one badge that shows thinking / idle / paused").
+  // Not online → the alive-table's own reading (rate-limited/needs-login/
+  // offline), no age (nothing to age). Online + paused → 'paused'
+  // overrides the turn-state reading, since a paused agent won't be
+  // thinking regardless of its last turn_state. Online + running →
+  // turn-state + age, same as before.
+  const primaryStatus =
+    state.status !== 'online'
+      ? { glyph: alive.glyph, text: alive.text, tone: alive.tone, tooltip: undefined as string | undefined }
+      : state.paused
+        ? { glyph: '⏸', text: 'paused', tone: 'warning' as BadgeTone, tooltip: undefined }
+        : {
+            glyph: turnDef.glyph,
+            text: `${turnDef.text} · ${stateAge}`,
+            tone: turnDef.tone,
+            tooltip: STATE_TOOLTIPS[effectiveTurnState],
+          };
   const ctx = tokenTotal(state.ctx_usage);
   const cost = tokenTotal(state.cost_usage);
 
@@ -186,11 +202,9 @@ export function Root() {
         pills={pills}
       >
         <StatusChips
-          aliveLabel={`${alive.glyph} ${alive.text}`}
-          aliveTone={alive.tone}
-          stateLabel={`${turnDef.glyph} ${turnDef.text} · ${stateAge}`}
-          stateTone={turnDef.tone}
-          stateTooltip={STATE_TOOLTIPS[effectiveTurnState]}
+          statusLabel={`${primaryStatus.glyph} ${primaryStatus.text}`}
+          statusTone={primaryStatus.tone}
+          statusTooltip={primaryStatus.tooltip}
           model={state.model}
           resolvedModel={state.resolved_model ?? undefined}
           availableModels={state.available_models}