feat: unify device auth + pairing

src/gateway/device-auth.ts

@@ -0,0 +1,24 @@
+export type DeviceAuthPayloadParams = {
+  deviceId: string;
+  clientId: string;
+  clientMode: string;
+  role: string;
+  scopes: string[];
+  signedAtMs: number;
+  token?: string | null;
+};
+
+export function buildDeviceAuthPayload(params: DeviceAuthPayloadParams): string {
+  const scopes = params.scopes.join(",");
+  const token = params.token ?? "";
+  return [
+    "v1",
+    params.deviceId,
+    params.clientId,
+    params.clientMode,
+    params.role,
+    scopes,
+    String(params.signedAtMs),
+    token,
+  ].join("|");
+}