feat(admin-auth): support username login and add dashboard logout

apps/admin/src/app/logout-button.tsx

@@ -0,0 +1,36 @@
+"use client"
+
+import { Button } from "@cms/ui/button"
+import { useRouter } from "next/navigation"
+import { useState } from "react"
+
+export function LogoutButton() {
+  const router = useRouter()
+  const [isBusy, setIsBusy] = useState(false)
+
+  async function handleLogout() {
+    setIsBusy(true)
+
+    try {
+      await fetch("/api/auth/sign-out", {
+        method: "POST",
+        headers: {
+          "content-type": "application/json",
+        },
+        body: JSON.stringify({ callbackURL: "/login" }),
+      })
+    } finally {
+      // biome-ignore lint/suspicious/noDocumentCookie: Temporary cookie fallback until role resolution no longer needs this cookie.
+      document.cookie = "cms_role=; Path=/; Max-Age=0; SameSite=Lax"
+      router.push("/login")
+      router.refresh()
+      setIsBusy(false)
+    }
+  }
+
+  return (
+    <Button type="button" onClick={() => void handleLogout()} disabled={isBusy} variant="secondary">
+      {isBusy ? "Signing out..." : "Sign out"}
+    </Button>
+  )
+}