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__/BackupRunsTable.test.tsx

@@ -0,0 +1,59 @@
+import { describe, it, expect } from "vitest";
+import { render, screen } from "@testing-library/react";
+import BackupRunsTable from "../BackupRunsTable";
+import type { BackupRun } from "../../types/backups";
+
+function run(overrides: Partial<BackupRun> = {}): BackupRun {
+	return {
+		id: "r1",
+		job_id: "job-1",
+		started_at: 1_700_000_000,
+		ended_at: null,
+		status: "success",
+		bytes_transferred: 2048,
+		duration_ms: 1500,
+		error_message: null,
+		details_json: null,
+		created_at: 1_700_000_000,
+		...overrides,
+	};
+}
+
+describe("BackupRunsTable", () => {
+	it("maps run status onto Badge variants per design §2.3", () => {
+		render(
+			<BackupRunsTable
+				runs={[
+					run({ id: "a", status: "success" }),
+					run({ id: "b", status: "failure" }),
+					run({ id: "c", status: "in_progress" }),
+				]}
+			/>,
+		);
+		expect(screen.getByText("success").getAttribute("data-variant")).toBe(
+			"success",
+		);
+		expect(screen.getByText("failure").getAttribute("data-variant")).toBe(
+			"destructive",
+		);
+		expect(screen.getByText("in_progress").getAttribute("data-variant")).toBe(
+			"warning",
+		);
+	});
+
+	it("renders the formatted duration and transferred size", () => {
+		render(
+			<BackupRunsTable
+				runs={[
+					run({
+						id: "fmt",
+						duration_ms: 1500,
+						bytes_transferred: 2048,
+					}),
+				]}
+			/>,
+		);
+		expect(screen.getByText("1.5s")).toBeInTheDocument();
+		expect(screen.getByText("2.0 KB")).toBeInTheDocument();
+	});
+});