fix(sdk): request the caught-up settle on AgentChat.reconnect()

The server-to-server AgentChat client's reconnect() now sends X-Peek-Settled,
so resuming an .out that is already at a turn-complete tail closes promptly
instead of holding the full SSE long-poll window. This matches the browser
transport's reconnectToStream and gives server-to-server consumers the same
fast tail-close. The active send-message path is unchanged (no peek, so it
never races a newly-triggered turn's first chunk).

Author: ericallam

.changeset/chat-session-caught-up-resume.md

@@ -3,4 +3,4 @@
 "@trigger.dev/sdk": patch
 ---
 
-Chat sessions now close a resumed stream as soon as it has caught up to the latest output, instead of holding the connection open for the full long-poll window. Reloading or reconnecting to an idle chat settles faster.
+Chat sessions now close a resumed stream as soon as it has caught up to the latest output, instead of holding the connection open for the full long-poll window. Reloading or reconnecting to an idle chat settles faster. This applies to the server-to-server `AgentChat` client's `reconnect()` too, not just the browser transport.

packages/trigger-sdk/src/v3/chat-client.ts

@@ -576,10 +576,18 @@ export class AgentChat<TAgent = unknown> {
     }
   }
 
-  /** Reconnect to the response stream (e.g. after a disconnect). */
+  /**
+   * Reconnect to the response stream (e.g. after a disconnect). Requests the
+   * caught-up settle probe (`X-Peek-Settled`) so a resumed stream already at a
+   * turn-complete tail closes promptly instead of holding the full SSE window,
+   * mirroring the browser transport's `reconnectToStream`.
+   */
   async reconnect(abortSignal?: AbortSignal): Promise<ReadableStream<UIMessageChunk> | null> {
     if (!this.state.started) return null;
-    return this.subscribeToSessionStream(abortSignal, { sendStopOnAbort: false });
+    return this.subscribeToSessionStream(abortSignal, {
+      sendStopOnAbort: false,
+      peekSettled: true,
+    });
   }
 
   // ─── Private ───────────────────────────────────────────────────
@@ -681,7 +689,7 @@ export class AgentChat<TAgent = unknown> {
 
   private subscribeToSessionStream(
     abortSignal: AbortSignal | undefined,
-    options?: { sendStopOnAbort?: boolean }
+    options?: { sendStopOnAbort?: boolean; peekSettled?: boolean }
   ): ReadableStream<UIMessageChunk> {
     const state = this.state;
     const accessToken = apiClientManager.accessToken ?? "";
@@ -743,6 +751,7 @@ export class AgentChat<TAgent = unknown> {
               ...(apiClientManager.branchName
                 ? { "x-trigger-branch": apiClientManager.branchName }
                 : {}),
+              ...(options?.peekSettled ? { "X-Peek-Settled": "1" } : {}),
             },
             signal: combinedSignal,
             timeoutInSeconds: this.streamTimeoutSeconds,