test: remove redundant cases and strengthen persistence, terminal and mobile checks (#33318)

Co-authored-by: OrcaWin <293788423+OrcaWin@users.noreply.github.com>

src/shared/agent-status-child-work-admission-activity.test.ts

@@ -118,7 +118,10 @@ describe('child-work admission of what a child is doing', () => {
 
   it('carries owner and residency through, and clears the operation of a parked child', () => {
     const { store, admission } = setup()
-    admission.announce(observation())
+    admission.announce(
+      observation({ operation: { toolName: 'Bash', basis: 'open', observedAt: 10 } })
+    )
+    expect(store.getChild('child-1')?.operation).toMatchObject({ toolName: 'Bash' })
     admission.announce(
       observation({
         aliases: [{ segmentId: 'segment-1', aliasKind: 'task_id', alias: 'shell-1' }],

src/shared/agent-status-child-work-admission.test.ts

@@ -118,6 +118,14 @@ describe('agent child-work admission', () => {
     ).toMatchObject({ accepted: true, childWorkId: 'child-1', created: false })
     expect(store.getChildren(parent)).toMatchObject([{ childWorkId: 'child-1', kind: 'agent' }])
     expect(store.getSnapshot().aliases.every((alias) => alias.kind === 'agent')).toBe(true)
+    expect(
+      admission.announce(
+        announce(parent, {
+          aliases: [{ segmentId: 'segment-1', aliasKind: 'tool_use_id', alias: 'tool-1' }],
+          observedAt: 13
+        })
+      )
+    ).toMatchObject({ accepted: true, childWorkId: 'child-1', created: false })
   })
 
   it('preserves the logical id and prior outcome across an explicit resume fence', () => {