feat(frontend): slice 3 — Backups cluster migration + nav/IA

Web UI rework.
- Migrate BackupAlertsTable, BackupJobsTable, BackupRunsTable,
  BackupsPage, BackupDashboardWidget off @mui (shadcn Table + Badge
  severity variants: success=chart-2, warning=chart-3, destructive)
- App.tsx IA: Backups now top-level nav (DatabaseBackup icon);
  Media surface primary at /media; /applications -> /media redirect
  in both route trees (mirrors /monitoring -> /observability)

Gate: build + lint + test green.

frontend/src/components/__tests__/BackupAlertsTable.test.tsx

@@ -0,0 +1,63 @@
+import { describe, it, expect, vi } from "vitest";
+import { render, screen } from "@testing-library/react";
+import userEvent from "@testing-library/user-event";
+import BackupAlertsTable from "../BackupAlertsTable";
+import type { BackupAlert } from "../../types/backups";
+
+function alert(overrides: Partial<BackupAlert> = {}): BackupAlert {
+	return {
+		id: "a1",
+		job_id: "job-1",
+		run_id: null,
+		alert_type: "failed_status",
+		severity: "warning",
+		message: "Run failed",
+		acknowledged: false,
+		resolved_at: null,
+		created_at: 1_700_000_000,
+		...overrides,
+	};
+}
+
+describe("BackupAlertsTable", () => {
+	it("maps alert severity onto Badge variants per design §2.3", () => {
+		render(
+			<BackupAlertsTable
+				alerts={[
+					alert({ id: "c", severity: "critical" }),
+					alert({ id: "w", severity: "warning" }),
+				]}
+				onAcknowledge={vi.fn()}
+			/>,
+		);
+		expect(screen.getByText("critical").getAttribute("data-variant")).toBe(
+			"destructive",
+		);
+		expect(screen.getByText("warning").getAttribute("data-variant")).toBe(
+			"warning",
+		);
+	});
+
+	it("calls onAcknowledge with the alert id when the button is clicked", async () => {
+		const onAcknowledge = vi.fn();
+		render(
+			<BackupAlertsTable
+				alerts={[alert({ id: "ack-me" })]}
+				onAcknowledge={onAcknowledge}
+			/>,
+		);
+		await userEvent.click(screen.getByRole("button", { name: "Acknowledge" }));
+		expect(onAcknowledge).toHaveBeenCalledTimes(1);
+		expect(onAcknowledge).toHaveBeenCalledWith("ack-me");
+	});
+
+	it("hides the acknowledge button for already-acknowledged alerts", () => {
+		render(
+			<BackupAlertsTable
+				alerts={[alert({ id: "done", acknowledged: true })]}
+				onAcknowledge={vi.fn()}
+			/>,
+		);
+		expect(screen.queryByRole("button", { name: "Acknowledge" })).toBeNull();
+	});
+});