Fix browser file operations and persist visible save times

Preserve JSON Content-Type when custom idempotency headers are supplied. Expose the latest accepted folder operation timestamp so browser saves remain visible before an agent runs and after all files are deleted.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

server/src/__tests__/work-folders.test.ts

@@ -57,6 +57,18 @@ describe("durable work folders", () => {
     expect(await textContent(f, "memory.md")).toBe("second");
     await expect(svc.write(f, { ...first, body: Buffer.from("different") })).rejects.toMatchObject({ status: 409 });
   });
+  it("retains the last accepted save time after all files are removed", async () => {
+    const f = await folder();
+    expect((await svc.list(f)).lastSavedAt).toBeNull();
+    await svc.write(f, { path: "note", body: Buffer.from("saved"), operationId: "write" });
+    const saved = (await svc.list(f)).lastSavedAt;
+    expect(saved).toEqual(expect.any(String));
+    await svc.remove(f, "note", "delete");
+    const listing = await svc.list(f);
+    expect(listing.files).toEqual([]);
+    expect(Date.parse(listing.lastSavedAt!)).toBeGreaterThanOrEqual(Date.parse(saved!));
+    expect((await svc.list(f, { trash: true })).lastSavedAt).toBe(listing.lastSavedAt);
+  });
   it("retains a deleted copy after the same path is recreated", async () => {
     const f = await folder();
     await svc.write(f, { path: "note", body: Buffer.from("deleted"), operationId: "one" });