fix(ai): the operator cap counts only tokens the operator paid for

The reservation compared the day's TOTAL against whichever ceiling the
chain resolved, and the chain walker's hop guard did the same. On an
account whose background jobs run on the user's own ChatGPT plan, both
saw a total the operator had not paid for: the chat refused at 06:42Z
with 513 539 tokens against the 200 000 operator ceiling, and the
fallback hop to the shared key was closed on the same arithmetic.

An operator-funded chain is now measured against `operator_tokens` and a
user-plan chain keeps its abuse ceiling on the total; the hop guard reads
the operator share too. A day of turns the user's own plan paid for can
no longer lock anyone out of the operator's ceiling.

tests/integration/coach-budget-owner.test.ts

@@ -153,6 +153,66 @@ describe("coach_usage.operator_tokens (real Postgres)", () => {
     expect(row?.operatorTokens).toBe(2_500);
   });
 
+  it("admits the operator's chat on a day his own plan filled", async () => {
+    const { reserveBudget, OPERATOR_COST_CAP } =
+      await import("@/lib/ai/coach/budget");
+    const userId = await seedUser();
+    const dateKey = "2026-09-11";
+
+    // The operator's 06:42Z lockout, reproduced: 1.2 M tokens on the day, of
+    // which only 150 k were served by the operator-funded key — the rest by
+    // `codex` on his own ChatGPT plan.
+    await getPrismaClient().coachUsage.create({
+      data: {
+        userId,
+        dateKey,
+        totalTokens: 1_200_000,
+        operatorTokens: 150_000,
+        messageCount: 240,
+      },
+    });
+
+    const res = await reserveBudget(
+      userId,
+      3_000,
+      dateKey,
+      OPERATOR_COST_CAP,
+      "operator",
+    );
+    expect(res.allowed).toBe(true);
+    expect(res.operatorAfter).toBe(153_000);
+  });
+
+  it("refuses once the operator-funded share reaches the operator cap", async () => {
+    const { reserveBudget, OPERATOR_COST_CAP } =
+      await import("@/lib/ai/coach/budget");
+    const userId = await seedUser();
+    const dateKey = "2026-09-11";
+
+    await getPrismaClient().coachUsage.create({
+      data: {
+        userId,
+        dateKey,
+        totalTokens: 1_200_000,
+        operatorTokens: OPERATOR_COST_CAP,
+        messageCount: 240,
+      },
+    });
+
+    const res = await reserveBudget(
+      userId,
+      3_000,
+      dateKey,
+      OPERATOR_COST_CAP,
+      "operator",
+    );
+    expect(res.allowed).toBe(false);
+
+    const row = await readRow(userId, dateKey);
+    expect(row?.totalTokens).toBe(1_200_000);
+    expect(row?.operatorTokens).toBe(OPERATOR_COST_CAP);
+  });
+
   it("refunds both counters when a refused reservation is rolled back", async () => {
     const { reserveBudget, OPERATOR_COST_CAP } =
       await import("@/lib/ai/coach/budget");