fix(sources): stop listing a source whose readings were all deleted

The in-use probe matched tombstoned readings, so a source stayed marked
on the priority ladder after every reading from it was deleted. Both
the read and the save response of the source-priority route go through
this one probe.

tests/integration/sources-in-use.test.ts

@@ -0,0 +1,61 @@
+/**
+ * The sources the Settings ladder lists, against real Postgres.
+ *
+ * A source counts while the account holds a live reading from it. Deleting
+ * readings tombstones them (`deletedAt`), so the probe has to skip the
+ * tombstones or a source whose readings were all deleted stays marked as in
+ * use for good.
+ */
+import { beforeEach, describe, expect, it } from "vitest";
+
+import { getPrismaClient, truncateAllTables } from "./setup";
+
+beforeEach(async () => {
+  await truncateAllTables(getPrismaClient());
+});
+
+async function seed() {
+  const prisma = getPrismaClient();
+  const user = await prisma.user.create({
+    data: {
+      username: "sources-in-use",
+      email: "sources-in-use@example.test",
+      role: "USER",
+    },
+  });
+  const reading = (source: "MANUAL" | "APPLE_HEALTH", minutes: number) =>
+    prisma.measurement.create({
+      data: {
+        userId: user.id,
+        type: "WEIGHT",
+        value: 80,
+        unit: "kg",
+        source,
+        measuredAt: new Date(Date.UTC(2026, 4, 12, 7, minutes)),
+      },
+    });
+  return { prisma, user, reading };
+}
+
+describe("getSourcesInUse", () => {
+  it("lists a source with a live reading", async () => {
+    const { user, reading } = await seed();
+    await reading("MANUAL", 0);
+    const { getSourcesInUse } =
+      await import("@/lib/integrations/sources-in-use");
+    expect(await getSourcesInUse(user.id)).toEqual(["MANUAL"]);
+  });
+
+  it("drops a source once every reading from it is deleted", async () => {
+    const { prisma, user, reading } = await seed();
+    const manual = await reading("MANUAL", 0);
+    await reading("APPLE_HEALTH", 1);
+    await prisma.measurement.update({
+      where: { id: manual.id },
+      data: { deletedAt: new Date() },
+    });
+    const { getSourcesInUse } =
+      await import("@/lib/integrations/sources-in-use");
+    expect(await getSourcesInUse(user.id)).toEqual(["APPLE_HEALTH"]);
+  });
+});