[BUG] MCP connector calls hang indefinitely from scheduled-task sessions (work fine interactively)

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) and this hasn't been reported yet
- [x] This is a single bug report (please file separate reports for different bugs)
- [x] I am using the latest version of Claude Code

### What's Wrong?

Tool calls to remote MCP connectors (confirmed with Gmail, Slack, and Asana) never complete when made from a scheduled-task session — no error, no timeout, no permission prompt, just permanent silence. The identical calls, with identical arguments, succeed immediately when made from a normal interactive session.

### What Should Happen?

The connector tool call in the scheduled-task session should return a result, the same way it does in an interactive session.

### Error Messages/Logs

```shell
None — that's part of the problem. No error surfaces anywhere; list_events on the hung session shows no error, no additional messages, and get_session's lastActivityAt simply stops advancing. No permission/approval prompt was visible either, confirmed by physically checking the session's window.
```

### Steps to Reproduce

1. In an interactive session, connect Gmail/Slack/Asana connectors and confirm a tool call works (e.g. Gmail's search_threads).
2. Create a scheduled task whose prompt calls that same connector tool.
3. Trigger the task manually ("Run now").
4. Watch the resulting session's transcript.

### Claude Model

Sonnet (default)

### Is this a regression?

No, this never worked

### Last Working Version

_No response_

### Claude Code Version

N/A — using the Claude desktop app's Code tab; claude --version isn't available as a separate CLI in this environment.

### Platform

Anthropic API

### Operating System

macOS

### Terminal/Shell

Terminal.app (macOS)

### Additional Information

Non-connector tool calls in the same scheduled-task session (Read, ToolSearch, the Artifact tool) worked fine — this appears specific to remote MCP connector calls, not scheduled tasks generally. Happy to provide exact session IDs / task prompt from my repro if useful.

Start by reproducing the scheduled task with the “Run now” entry point, then compare its transcript, list_events output, and get_session lastActivityAt with an interactive MCP call. The issue names no source files or tests, so the implementation entry point and a suitable regression test still need to be located; done means remote connector calls return results instead of hanging silently.

Written by the indexing model from the issue text.