fix(terminal): fold only bare identity frames into the group token

A legacy "π - <session> - <cwd>" title is Pi-compatible too, so folding
every profile match collapsed two different sessions to the same signature
and suppressed the change outright — reintroducing #16093 through the
churn signature.

Fold only exact bare identity frames, matched per wrapper segment, so
semantic session titles keep comparing on their own text.

Co-authored-by: Seongho.Bak <49228032+psh4607@users.noreply.github.com>

src/renderer/src/store/slices/repro-omp-pi-alternating-title-frame-churn.test.ts

@@ -224,6 +224,27 @@ describe('OMP-owned tab title across interleaved OMP/Pi spinner frames', () => {
     expect(store.getState().runtimePaneTitlesByTabId[TAB_ID]?.[PANE_ID]).toBe('⠙ Codex')
   })
 
+  // Why: a legacy "π - <session> - <cwd>" frame is Pi-compatible too, but its text is real session
+  // state. Folding it into the group token would make two different sessions compare equal and
+  // suppress the change outright — the #16093 complaint, reintroduced through the signature.
+  it('still commits a change between two semantic session titles', () => {
+    const store = createTestStore()
+    seedOmpTab(store)
+
+    store.getState().setRuntimePaneTitle(TAB_ID, PANE_ID, 'π - fixing the sidebar - orca')
+    let commits = 0
+    const unsubscribe = store.subscribe(() => {
+      commits += 1
+    })
+    store.getState().setRuntimePaneTitle(TAB_ID, PANE_ID, 'π - writing the tests - orca')
+    unsubscribe()
+
+    expect(commits).toBe(1)
+    expect(store.getState().runtimePaneTitlesByTabId[TAB_ID]?.[PANE_ID]).toBe(
+      'π - writing the tests - orca'
+    )
+  })
+
   // Why: owner-pinning must stay scoped to bare identity frames. A semantic session title carries
   // text no agent profile can reproduce, so relabeling it to "OMP ready" would lose real
   // information — the complaint in #16093, which this fix must not reintroduce.

src/shared/agent-title-owner.ts

@@ -5,7 +5,10 @@ import {
   SYNTHETIC_AGENT_TITLE_PROFILES,
   type SyntheticAgentTitleProfile
 } from './synthetic-agent-title'
-import { isLegacyPiCompatibleTitle } from './pi-compatible-synthetic-title'
+import {
+  getPiCompatibleSyntheticAgentLabel,
+  isLegacyPiCompatibleTitle
+} from './pi-compatible-synthetic-title'
 import { getWrapperTitleSegments } from './terminal-title-wrapper-segments'
 
 type TitleProfileMatch = {
@@ -67,20 +70,30 @@ export function hasCompatibleAgentTitleIdentity(title: string): boolean {
 }
 
 /**
- * Replaces the agent-identity segment of a title with its identity-group name, leaving any
- * wrapper prefix intact ("zsh | ⠋ Pi" and "zsh | ⠋ OMP" both become "zsh | pi-compatible").
+ * Replaces a bare agent-identity frame with its identity-group name, leaving any wrapper prefix
+ * intact ("zsh | ⠋ Pi" and "zsh | ⠙ OMP" both become "zsh | pi-compatible").
  *
  * Why: members of a group are the same agent to a pane — OMP wraps Pi and both harnesses emit
  * frames — so which one a frame names is decoration, not state. Callers comparing consecutive
- * frames need them to compare equal; callers rendering the title must not use this.
+ * frames need those to compare equal; callers rendering the title must not use this.
+ *
+ * Why only bare frames: a legacy "π - <session> - <cwd>" title is also Pi-compatible, but its
+ * text is real session state. Folding it would make two different sessions compare equal and
+ * suppress the change outright (#16093).
  */
 export function collapseCompatibleAgentTitleIdentity(title: string): string {
-  const source = getProfileForTitle(title)
-  const group = source?.profile.titleIdentityGroup
-  if (!group) {
-    return title
+  for (const segment of getWrapperTitleSegments(title)) {
+    const label = getPiCompatibleSyntheticAgentLabel(segment)
+    const group = label
+      ? SYNTHETIC_AGENT_TITLE_PROFILES[label.toLowerCase()]?.titleIdentityGroup
+      : undefined
+    if (!group) {
+      continue
+    }
+    const at = title.lastIndexOf(segment)
+    return at === -1 ? group : title.slice(0, at) + group
   }
-  return title.replace(source.sourceTitle, group)
+  return title
 }
 
 /**