fix(pi): stop OMP tab icon flashing to Pi while working (#9077)

OMP runs as a `shell → omp → pi` process tree and Orca recognizes both
`omp` and `pi` as distinct agents, so the foreground-process reader
alternates between reporting the two across command boundaries. In
`resolveTabAgentFromSignals` every identity signal is re-owned onto the
pane's durable owner within its title-identity group (pi and omp share
one) — except the process signal, which was consumed raw. Because it
ranks above launchAgent, each `pi` read repainted an OMP-owned tab's icon
to the Pi glyph and the next read flipped it back.

Re-own the process signal the same way the hook and title signals already
are, so a same-group read collapses onto the owner while a genuine
cross-group process (e.g. Codex) still stands and can reclaim a reused
pane. The tab title text was unaffected — its owner resolution already
excludes the process signal — so this is icon-only.

Adds regression coverage for the oscillation, the mirrored/restored pane
(launchAgent gone, durable hook record), and the cross-group scope guard.

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

@@ -132,6 +132,64 @@ describe('resolveTabAgentFromSignals — Pi/OMP identity', () => {
     expect(afterHookCleared).toBe('omp')
   })
 
+  it('does not flap between OMP and Pi as the foreground process oscillates', () => {
+    // The reported flicker: OMP wraps Pi (`shell → omp → pi`), so the foreground
+    // reader alternates between reporting `omp` and `pi` at command boundaries.
+    // The process signal outranks launchAgent, so without owner-normalization the
+    // OMP-owned tab's icon flips to Pi on every `pi` read. Both reads must land on
+    // the launched owner.
+    const readsPi = resolveTabAgentFromSignals({
+      hasObservedAgentSignal: true,
+      isRemote: false,
+      title: '⠋ OMP',
+      hookAgent: null,
+      processAgent: 'pi',
+      launchAgent: 'omp'
+    })
+    const readsOmp = resolveTabAgentFromSignals({
+      hasObservedAgentSignal: true,
+      isRemote: false,
+      title: '⠋ OMP',
+      hookAgent: null,
+      processAgent: 'omp',
+      launchAgent: 'omp'
+    })
+    expect(readsPi).toBe('omp')
+    expect(readsOmp).toBe('omp')
+  })
+
+  it('re-owns a Pi foreground read to a durable OMP identity when launchAgent is gone', () => {
+    // A mirrored/restored OMP pane keeps only its completed-hook identity; a `pi`
+    // foreground read (OMP's nested child) must not repaint it to Pi.
+    expect(
+      resolveTabAgentFromSignals({
+        hasObservedAgentSignal: true,
+        isRemote: false,
+        title: '⠋ OMP',
+        hookAgent: null,
+        focusedCompletedHookAgent: 'omp',
+        processAgent: 'pi',
+        launchAgent: undefined
+      })
+    ).toBe('omp')
+  })
+
+  it('still lets a genuine cross-group foreground process reclaim a reused OMP pane', () => {
+    // Scope guard: a different-group process (Codex is not Pi-compatible) is
+    // real-time proof the pane was reused, so it overrides the OMP launch owner
+    // instead of collapsing onto it.
+    expect(
+      resolveTabAgentFromSignals({
+        hasObservedAgentSignal: true,
+        isRemote: false,
+        title: 'zsh',
+        hookAgent: null,
+        processAgent: 'codex',
+        launchAgent: 'omp'
+      })
+    ).toBe('codex')
+  })
+
   it('keeps a launchAgent-less Pi pane on Pi and rejects a stale OMP session record', () => {
     // The fallback must not over-reach: a genuine Pi pane (recent Pi hook) stays
     // Pi even if a stale hibernated OMP record is present.

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

@@ -168,7 +168,13 @@ export function resolveTabAgentFromSignals(args: {
     processShellForeground: args.processShellForeground
   })
   const activeLaunchAgent = launchedAgentExited ? null : launchAgent
-  const processAgent = args.processAgent ?? null
+  // Why: the foreground process, like the hook and title signals, must be
+  // re-owned within its title-identity group. OMP wraps Pi as `shell → omp → pi`,
+  // so the foreground reader oscillates between reporting `omp` and `pi` across
+  // command boundaries; taken raw it outranks launchAgent and flips an OMP-owned
+  // tab's icon between the two glyphs. Re-owning collapses the same-group read
+  // onto the durable owner while a genuine cross-group process still stands.
+  const processAgent = resolveSignalAgentForLaunchOwner(args.processAgent, owner)
   const sleepingSessionAgent = args.sleepingSessionAgent ?? null
   // Identity-first precedence. The live focused hook is ground truth while the
   // agent works; process identity covers agents with neither hook nor title; the
@@ -199,7 +205,8 @@ export function resolveTabAgentFromSignals(args: {
  * 2. Process identity — the recognized foreground process, read at OSC 133
  *    command boundaries (local panes only); covers agents that emit neither
  *    hooks nor titles, and its shell-foreground mark is title-independent exit
- *    evidence.
+ *    evidence. Re-owned within its title-identity group, so OMP's nested `pi`
+ *    child (the `shell → omp → pi` tree) cannot flip the icon back to Pi.
  * 3. Title — only as a reuse override (it names a DIFFERENT-group agent than the
  *    pane's known identity, proving reuse) or as a legacy standalone identity
  *    when the pane has no hook. Within the same title-identity group it carries