Address review: don't suppress sibling identity on focused exit

The focused pane's local shell-exit evidence (`idleIdentitySuppressed`) also
nulled the sibling split-pane's idle identity, so a focused pane returning to
its shell could hide a still-valid idle sibling agent. Scope the suppression to
the focused pane only. Adds coverage for the sibling-kept-on-focused-exit case
and for a launchAgent-less pane whose live Pi hook stays Pi.

src/renderer/src/lib/use-tab-agent-pi-identity.test.ts

@@ -222,6 +222,46 @@ describe('resolveTabAgentFromSignals — identity vs liveness', () => {
     ).toBe('claude')
   })
 
+  it('keeps a launchAgent-less pane with a live Pi hook stable on Pi', () => {
+    // A launchless pane whose live hook reports Pi resolves to Pi and stays Pi
+    // when the hook clears (the completed record is Pi too) — no flip to OMP.
+    expect(
+      resolveTabAgentFromSignals({
+        hasObservedAgentSignal: true,
+        isRemote: true,
+        title: '⠋ Pi',
+        hookAgent: 'pi',
+        launchAgent: undefined
+      })
+    ).toBe('pi')
+    expect(
+      resolveTabAgentFromSignals({
+        hasObservedAgentSignal: true,
+        isRemote: true,
+        title: '⠋ Pi',
+        hookAgent: null,
+        focusedCompletedHookAgent: 'pi',
+        launchAgent: undefined
+      })
+    ).toBe('pi')
+  })
+
+  it('keeps a sibling idle identity when the focused pane returns to its shell', () => {
+    // Focused pane's local shell-exit evidence must not clear the sibling's idle
+    // identity — the sibling agent is still there.
+    expect(
+      resolveTabAgentFromSignals({
+        hasObservedAgentSignal: true,
+        isRemote: false,
+        title: 'zsh',
+        hookAgent: null,
+        focusedCompletedHookAgent: 'claude',
+        siblingCompletedHookAgent: 'gemini',
+        launchAgent: undefined
+      })
+    ).toBe('gemini')
+  })
+
   it('does not let a sibling pane re-own the focused pane ambiguous Pi title', () => {
     // A split-pane sibling running OMP says nothing about which Pi-variant the
     // focused pane runs; the focused pane's own Pi title must stay Pi.

src/renderer/src/lib/use-tab-agent.ts

@@ -120,9 +120,13 @@ export function resolveTabAgentFromSignals(args: {
   const idleFocusedIdentity = idleIdentitySuppressed
     ? null
     : resolveSignalAgentForLaunchOwner(args.focusedCompletedHookAgent, owner)
-  const idleSiblingIdentity = idleIdentitySuppressed
-    ? null
-    : resolveSignalAgentForLaunchOwner(args.siblingCompletedHookAgent, launchAgent)
+  // Why: `idleIdentitySuppressed` is the FOCUSED pane's own exit evidence, so it
+  // must not clear a sibling split-pane's idle identity — a focused pane back at
+  // its shell says nothing about whether the sibling's agent has exited.
+  const idleSiblingIdentity = resolveSignalAgentForLaunchOwner(
+    args.siblingCompletedHookAgent,
+    launchAgent
+  )
 
   // The title carries identity in only two roles: (a) a reuse override — it
   // names a DIFFERENT-group agent than the pane's known identity, proving the