fix(diagnostics): say which read failed, and let Live restart

- "Load older" is not offered off a loading filter's placeholder rows,
  whose cursor belongs to the previous filter.
- A failed older page, stale rows and missing counts each get their own
  message (HU/EN).
- Live shows as off once a failed read stopped the polling; pressing it
  again reads now.

frontend/src/components/AdminLogs.dom.test.tsx

@@ -197,6 +197,44 @@ describe("AdminLogs", () => {
     const reads = logsMock.mock.calls.length;
     await act(async () => vi.advanceTimersByTimeAsync(12000));
     expect(logsMock.mock.calls.length).toBe(reads);
+    // The button says polling stopped, and pressing it reads again.
+    const liveButton = screen.getByRole("button", { name: "adminLogs.live" });
+    expect(liveButton.getAttribute("aria-pressed")).toBe("false");
+    fireEvent.click(liveButton);
+    await settle();
+    expect(logsMock.mock.calls.length).toBe(reads + 1);
+  });
+
+  it("a failed older page says so, not that the list is out of date", async () => {
+    logsMock.mockImplementation(async (_q, before) => {
+      if (before !== null) throw new Error("500");
+      return { items: [row(2)], accounts: {}, next_cursor: "c1" };
+    });
+    renderConsole();
+    await waitFor(() => expect(lines()).toHaveLength(1));
+
+    fireEvent.click(screen.getByRole("button", { name: "adminLogs.older" }));
+
+    expect((await screen.findByRole("alert")).textContent).toContain("adminLogs.olderFailed");
+  });
+
+  it("offers no older page while a filter change loads", async () => {
+    let landErrors!: (page: LogPage) => void;
+    logsMock.mockImplementation((q) =>
+      q.levels
+        ? new Promise<LogPage>((resolve) => (landErrors = resolve))
+        : Promise.resolve({ items: [row(2)], accounts: {}, next_cursor: "c1" }),
+    );
+    renderConsole();
+    await waitFor(() => expect(lines()).toHaveLength(1));
+    expect(screen.queryByRole("button", { name: "adminLogs.older" })).toBeTruthy();
+
+    fireEvent.click(screen.getByRole("button", { name: /settings\.myLog\.filters\.error/ }));
+    await waitFor(() => expect(landErrors).toBeTypeOf("function"));
+
+    // The rows on screen are the previous filter's: their cursor is not this list's.
+    expect(screen.queryByRole("button", { name: "adminLogs.older" })).toBeNull();
+    await act(async () => landErrors({ items: [row(1)], accounts: {}, next_cursor: null }));
   });
 
   it("copies every loaded line, oldest first", async () => {