feat(nutrients): tell the account holder when a sync arrived but nothing landed

GET /api/nutrients now looks up the most recent nutrient.batch.ingest
audit row when the window is genuinely empty, and surfaces it as
lastAttempt only when that call landed nothing (inserted === 0 &&
updated === 0). A real success elsewhere is left alone, so an empty
window for an unrelated reason never gets reframed as a failure.

The lookup runs on the zero-rows path only, never on the happy path,
and stays counts-and-reason-codes only - no user-typed content, no
per-entry health values. The reason code never reaches the page as
text: each of the four closed skip reasons maps to its own human
sentence, and the two that have no useful action for the account
holder (unit_mismatch, upsert_failed) say plainly that the entries
couldn't be stored rather than inventing advice. day_invalid is the
one case worth naming a real cause for - a clock or time zone mismatch
on the sending side - without claiming it was a phone, since any
token holder can call this route.

This depends on AuditLog retention: cleanupOldAuditLogs prunes rows
past 365 days by default, so a dormant account's last failed attempt
can age out and the explanation silently reverts to the plain empty
state. Documented at the lookup for whoever next touches that job.

tests/integration/nutrients-batch.test.ts

@@ -301,4 +301,83 @@ describe("GET /api/nutrients (real Postgres)", () => {
     const res = await GET(new NextRequest("http://localhost/api/nutrients"));
     expect(res.status).toBe(403);
   });
+
+  // The account holder's only signal that a sync ever arrived: when the
+  // window is genuinely empty AND the most recent nutrient-batch call
+  // landed nothing, the read surfaces why instead of a bare empty state.
+  it("surfaces the last failed attempt when the window is genuinely empty", async () => {
+    const { POST } = await import("@/app/api/nutrients/batch/route");
+    const { GET } = await import("@/app/api/nutrients/route");
+
+    await POST(
+      postReq({
+        entries: [
+          { day: recentDay(1), nutrient: "vitamin_d", unit: "mg", amount: 20 },
+        ],
+      }),
+    );
+
+    const res = await GET(
+      new NextRequest("http://localhost/api/nutrients?days=14"),
+    );
+    const json = (await res.json()) as {
+      data: { nutrients: unknown[]; lastAttempt: { topReason: string } | null };
+    };
+    expect(json.data.nutrients).toHaveLength(0);
+    expect(json.data.lastAttempt).toMatchObject({
+      topReason: "unit_mismatch",
+    });
+  });
+
+  it("omits lastAttempt entirely once the window has data", async () => {
+    const { POST } = await import("@/app/api/nutrients/batch/route");
+    const { GET } = await import("@/app/api/nutrients/route");
+
+    await POST(
+      postReq({
+        entries: [
+          { day: recentDay(1), nutrient: "caffeine", unit: "mg", amount: 250 },
+        ],
+      }),
+    );
+
+    const res = await GET(
+      new NextRequest("http://localhost/api/nutrients?days=14"),
+    );
+    const json = (await res.json()) as {
+      data: { nutrients: unknown[]; lastAttempt: unknown };
+    };
+    expect(json.data.nutrients).toHaveLength(1);
+    expect(json.data.lastAttempt).toBeNull();
+  });
+
+  // A last attempt that actually SUCCEEDED must never be reframed as a
+  // failure just because the window is empty for an unrelated reason
+  // (here: the stored row was removed after the fact). Showing a failure
+  // notice over a real success is the exact false claim this feature
+  // exists to prevent.
+  it("stays silent when the last recorded attempt succeeded, even if the window is now empty", async () => {
+    const { POST } = await import("@/app/api/nutrients/batch/route");
+    const { GET } = await import("@/app/api/nutrients/route");
+
+    await POST(
+      postReq({
+        entries: [
+          { day: recentDay(1), nutrient: "caffeine", unit: "mg", amount: 250 },
+        ],
+      }),
+    );
+    await getPrismaClient().nutrientIntakeDay.deleteMany({
+      where: { userId: OPTED_IN_USER },
+    });
+
+    const res = await GET(
+      new NextRequest("http://localhost/api/nutrients?days=14"),
+    );
+    const json = (await res.json()) as {
+      data: { nutrients: unknown[]; lastAttempt: unknown };
+    };
+    expect(json.data.nutrients).toHaveLength(0);
+    expect(json.data.lastAttempt).toBeNull();
+  });
 });