feat: show per-step OpenRouter cost on the Trajectory tab

Extend the openRouterCost projection with a per-step priced-cost map
keyed by turn:step so surfaces can render spend without re-pricing, and
have the Trajectory view read it through the framework useProjection seat:
each priced assistant step shows its USD cost on the request boundary chip
and in the inspector summary, while unpriced steps stay blank. Also fix a
pre-existing exactOptionalPropertyTypes error in extractCacheRates that the
host typecheck surfaced.

packages/client/ui-trajectory/tests/table.client.spec.tsx

@@ -871,4 +871,46 @@ describe('TrajectoryTable', () => {
     expect(screen.getByRole('row', { name: /TOOL/ }).getAttribute('aria-selected')).toBe('false')
     expect(onInspectApplied).not.toHaveBeenCalled()
   })
+
+  it('shows a host-priced step cost on the request boundary and in the summary', () => {
+    render(
+      <TrajectoryTable
+        turns={TURNS}
+        requestNumbers={[{
+          turn: 1, step: 1, group: 'Step 1', number: 1, seq: 1,
+          stepCostUsd: 0.0028,
+        }]}
+        {...FOLD_PROPS}
+      />,
+    )
+    const chip = screen.getByRole('button', { name: 'Request #1 · $0.0028' })
+    expect(chip).toBeTruthy()
+    fireEvent.click(chip)
+    expect(screen.getByText('Cost')).toBeTruthy()
+    expect(screen.getByText('$0.0028')).toBeTruthy()
+  })
+
+  it('formats step costs above a cent with the currency format', () => {
+    render(
+      <TrajectoryTable
+        turns={TURNS}
+        requestNumbers={[{
+          turn: 1, step: 1, group: 'Step 1', number: 1, seq: 1,
+          stepCostUsd: 1.234,
+        }]}
+        {...FOLD_PROPS}
+      />,
+    )
+    const chip = screen.getByRole('button', { name: 'Request #1 · $1.23' })
+    expect(chip).toBeTruthy()
+    fireEvent.click(chip)
+    expect(screen.getByText('Cost')).toBeTruthy()
+    expect(screen.getByText('$1.23')).toBeTruthy()
+  })
+
+  it('omits the cost row when the step was not priced', () => {
+    render(<TrajectoryTable turns={TURNS} {...FOLD_PROPS} />)
+    fireEvent.click(screen.getByRole('button', { name: 'Request #1' }))
+    expect(screen.queryByText('Cost')).toBeNull()
+  })
 })

packages/client/ui-trajectory/tests/views.client.spec.tsx

@@ -255,7 +255,8 @@ function mount(slots: SlotRegistry, nodes: ConversationSnapshot['nodes'] = NODES
     return (
       <View
         {...injectedProps}
-        {...({ sessionId: SID, useSession, useSessions: emptySessions(), useWorkspaces: emptyWorkspaces() } as unknown as ConvViewProps)}
+        {...({ sessionId: SID, useSession, useProjection: () => undefined,
+          useSessions: emptySessions(), useWorkspaces: emptyWorkspaces() } as unknown as ConvViewProps)}
         key={key}
       />
     )
@@ -1199,6 +1200,32 @@ describe('TrajectoryView state', () => {
     )).toBeTruthy()
   })
 
+  it('attaches the per-step OpenRouter cost from the openRouterCost projection', () => {
+    render(
+      <TrajectoryView
+        {...standaloneProps(NODES)}
+        {...standaloneHistory(historySnapshot(NODES))}
+        {...standaloneDuration()}
+        useProjection={((key: string) => (key === 'openRouterCost'
+          ? {
+            totalUsd: 0.00336,
+            pricedSteps: 2,
+            unknownModelSteps: 0,
+            steps: { '1:1': 0.0028 },
+            currency: 'USD',
+          }
+          : undefined)) as never}
+      />,
+    )
+    // The turn-1/step-1 request is priced; the turn-2/step-1 one is not.
+    expect(screen.getByRole('button', { name: 'Request #1 · $0.0028' })).toBeTruthy()
+    expect(screen.queryByRole('button', { name: 'Request #2 · $0.0028' })).toBeNull()
+    // The summary of the priced step shows its cost.
+    fireEvent.click(screen.getByRole('button', { name: 'Request #1 · $0.0028' }))
+    expect(screen.getByText('Cost')).toBeTruthy()
+    expect(screen.getByText('$0.0028')).toBeTruthy()
+  })
+
 })
 
 describe('node half', () => {