fix(desktop-sdk): type focusedUsage as Partial<UsageStats>, fix expect arity

ClientSessionState.usage is Partial<UsageStats> (app/types.ts) — the
backend streams whichever fields changed — so the computed produces
ReadableAtom<Partial<UsageStats> | null>. Annotate the entry honestly
instead of claiming full UsageStats, and document the fallback rule for
plugin authors. Also collapse the three-argument expect() calls in the
contract test (vitest takes one message arg). Addresses triage review on
PR #80461.

apps/desktop/src/sdk/host-state.test.ts

@@ -38,9 +38,9 @@ describe('host.state focused-session atoms', () => {
     for (const key of ['focusedSessionId', 'focusedStoredSessionId', 'focusedUsage'] as const) {
       const store = host.state[key]
       expect(store, key).toBeDefined()
-      expect(typeof store.get, 'function', key)
-      expect(typeof store.listen, 'function', key)
-      expect(typeof store.subscribe, 'function', key)
+      expect(typeof store.get, key).toBe('function')
+      expect(typeof store.listen, key).toBe('function')
+      expect(typeof store.subscribe, key).toBe('function')
     }
   })
 
@@ -74,6 +74,7 @@ describe('host.state focused-session atoms', () => {
         title: id
       })
     }
+
     tree.declareDefaultTree(
       model.split('row', [
         model.group(['workspace'], { active: 'workspace', id: 'grp-main' }),

apps/desktop/src/sdk/index.ts

@@ -145,8 +145,10 @@ export const host = {
     focusedStoredSessionId: readonlyAtom<null | string>($focusedStoredSessionId),
     /** Live usage snapshot of the focused session (`context_used` /
      *  `context_max` / `context_percent`, token counts, `cost_usd`) —
-     *  streamed by the backend, no RPC needed. Null while unresolved. */
-    focusedUsage: readonlyAtom<null | UsageStats>($focusedUsage),
+     *  streamed by the backend, no RPC needed. Null while unresolved.
+     *  Partial: the backend streams whichever fields changed, so every
+     *  field read needs a fallback. */
+    focusedUsage: readonlyAtom<null | Partial<UsageStats>>($focusedUsage),
     /** Gateway socket state: 'idle' | 'connecting' | 'open' | …. Not turn-busy. */
     gateway: readonlyAtom<string>($gatewayState),
     /** Current main model slug. */