fix(ai): background generation cannot spend the interactive day

The automatic generators — status and reference cards, the briefing, the
arrival reaction, the nudge, document summaries and the index backfill —
reserved against the same ceiling as the chat. On the operator's account
that meant 150-330 ledger rows a day, 172 metric generations before
06:42Z, and a ceiling already spent when he opened the chat.

Every background surface now reserves through
`resolveDailyCapFor("job", chain)`: half the cost owner's ceiling, all
job surfaces together. The interactive routes keep the whole ceiling, so
a day of background work can no longer take the user's own away.

src/app/api/documents/inbound/[id]/chat/__tests__/route.test.ts

@@ -51,6 +51,7 @@ vi.mock("@/lib/ai/coach/budget", () => ({
   reserveBudget: vi.fn().mockResolvedValue({ allowed: true, reserved: 600 }),
   reconcileSpend: vi.fn().mockResolvedValue(undefined),
   resolveDailyCap: vi.fn(() => 100000),
+  resolveDailyCapFor: vi.fn(() => 100000),
   resolveCostOwner: vi.fn(() => "operator" as const),
 }));
 vi.mock("@/lib/ai/provider-runner", () => ({

src/app/api/documents/inbound/[id]/extract/__tests__/route.test.ts

@@ -69,6 +69,7 @@ vi.mock("@/lib/ai/coach/budget", () => ({
   reserveBudget: vi.fn().mockResolvedValue({ allowed: true, reserved: 1 }),
   reconcileSpend: vi.fn().mockResolvedValue(undefined),
   resolveDailyCap: vi.fn(() => 1000),
+  resolveDailyCapFor: vi.fn(() => 1000),
   resolveCostOwner: vi.fn(() => "operator" as const),
 }));
 vi.mock("@/lib/documents/extract", () => ({

src/app/api/documents/inbound/[id]/index/__tests__/route.test.ts

@@ -52,6 +52,7 @@ vi.mock("@/lib/ai/coach/budget", () => ({
   reserveBudget: vi.fn().mockResolvedValue({ allowed: true, reserved: 1 }),
   reconcileSpend: vi.fn().mockResolvedValue(undefined),
   resolveDailyCap: vi.fn(() => 1000),
+  resolveDailyCapFor: vi.fn(() => 1000),
   resolveCostOwner: vi.fn(() => "operator" as const),
 }));
 vi.mock("@/lib/modules/gate", () => ({

src/app/api/documents/inbound/[id]/suggest/__tests__/route.test.ts

@@ -40,6 +40,7 @@ vi.mock("@/lib/ai/coach/budget", () => ({
   reserveBudget: vi.fn().mockResolvedValue({ allowed: true, reserved: 1 }),
   reconcileSpend: vi.fn().mockResolvedValue(undefined),
   resolveDailyCap: vi.fn(() => 1000),
+  resolveDailyCapFor: vi.fn(() => 1000),
   resolveCostOwner: vi.fn(() => "operator" as const),
 }));
 vi.mock("@/lib/modules/gate", () => ({

src/app/api/documents/inbound/[id]/summary/__tests__/route.test.ts

@@ -53,6 +53,7 @@ vi.mock("@/lib/ai/coach/budget", () => ({
   reserveBudget: vi.fn().mockResolvedValue({ allowed: true, reserved: 1 }),
   reconcileSpend: vi.fn().mockResolvedValue(undefined),
   resolveDailyCap: vi.fn(() => 1000),
+  resolveDailyCapFor: vi.fn(() => 1000),
   resolveCostOwner: vi.fn(() => "operator" as const),
 }));
 vi.mock("@/lib/modules/gate", () => ({