refactor(remote): extract shared registerWithCloud() helper

Registration HTTP logic was duplicated three times across listen.ts
(initial + re-register) and listen.tsx. Extracted into
listen-register.ts with proper error handling for non-JSON responses,
response shape validation, and 5 focused tests. Removes ~110 lines
of duplication.

🐛 Generated with [Letta Code](https://letta.com)

Co-Authored-By: Letta <noreply@letta.com>

src/websocket/listen-register.ts

@@ -0,0 +1,81 @@
+/**
+ * Shared registration helper for letta remote / /remote command.
+ * Owns the HTTP request contract and error handling; callers own UX strings and logging.
+ */
+
+export interface RegisterResult {
+  connectionId: string;
+  wsUrl: string;
+}
+
+export interface RegisterOptions {
+  serverUrl: string;
+  apiKey: string;
+  deviceId: string;
+  connectionName: string;
+}
+
+/**
+ * Register this device with the Letta Cloud environments endpoint.
+ * Throws on any failure with an error message suitable for wrapping in caller-specific context.
+ */
+export async function registerWithCloud(
+  opts: RegisterOptions,
+): Promise<RegisterResult> {
+  const registerUrl = `${opts.serverUrl}/v1/environments/register`;
+
+  const response = await fetch(registerUrl, {
+    method: "POST",
+    headers: {
+      "Content-Type": "application/json",
+      Authorization: `Bearer ${opts.apiKey}`,
+      "X-Letta-Source": "letta-code",
+    },
+    body: JSON.stringify({
+      deviceId: opts.deviceId,
+      connectionName: opts.connectionName,
+    }),
+  });
+
+  if (!response.ok) {
+    let detail = `HTTP ${response.status}`;
+    const text = await response.text().catch(() => "");
+    if (text) {
+      try {
+        const parsed = JSON.parse(text) as { message?: string };
+        if (parsed.message) {
+          detail = parsed.message;
+        } else {
+          detail += `: ${text.slice(0, 200)}`;
+        }
+      } catch {
+        detail += `: ${text.slice(0, 200)}`;
+      }
+    }
+    throw new Error(detail);
+  }
+
+  let body: unknown;
+  try {
+    body = await response.json();
+  } catch {
+    throw new Error(
+      "Server returned non-JSON response — is the server running?",
+    );
+  }
+
+  const result = body as Record<string, unknown>;
+  if (
+    typeof result.connectionId !== "string" ||
+    typeof result.wsUrl !== "string"
+  ) {
+    throw new Error(
+      "Server returned unexpected response shape (missing connectionId or wsUrl)",
+    );
+  }
+
+  return {
+    connectionId: result.connectionId,
+    wsUrl: result.wsUrl,
+  };
+}