[BUG] Slack connector shows "Connected" in Settings but is invisible to routines/MCP authorization

### 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?

Summary

Slack shows as Connected in claude.ai → Settings → Connectors (checkmark, type "Web"), but two independent systems within Claude Code still treat it as unauthorized:

Cloud routine creation (/schedule, RemoteTrigger API) — the available-connectors list for attaching to a scheduled routine returns empty. Slack does not appear as attachable.
In-session MCP tool authorization — plugin:productivity:slack is flagged as requiring authentication before its tools can be used, separate from the routine check above.

What I tried

Reconnected Slack from the Connectors settings page — no change.
Re-checked the routine connector list three times over the course of the conversation — identical empty result each time.
Updated the Claude Desktop app (first attempt failed to complete, second attempt succeeded) — no change after full update.
Other connectors in the same Settings list (Gmail, Google Drive, HubSpot) show the same "Connected" checkmark status; not yet tested whether they have the same gap or work correctly for routines (worth checking for comparison).

Environment

Claude Desktop app, macOS, version 1.34493.1

### What Should Happen?

A connector shown as "Connected" in Settings should be available for both routine attachment and MCP tool use without a separate authorization step.

### Error Messages/Logs

```shell

```

### Steps to Reproduce

Confirm Slack is connected at claude.ai → Settings → Connectors (screenshot attached — checkmark shown).
In Claude Code, attempt to create a scheduled routine that attaches a Slack connector.
Observe the available-connectors list returns empty.
Separately, observe plugin:productivity:slack listed as requiring authentication in the session's tool-availability list.

### Claude Model

Sonnet (default)

### Is this a regression?

Yes, this worked in a previous version

### Last Working Version

_No response_

### Claude Code Version

1.34493.1

### Platform

Anthropic API

### Operating System

macOS

### Terminal/Shell

Terminal.app (macOS)

### Additional Information

_No response_

Start by reproducing the connection at claude.ai → Settings → Connectors, then compare the available-connectors list during scheduled routine creation with the session tool-availability list for plugin:productivity:slack. Check whether the same gap affects Gmail, Google Drive, or HubSpot. Done means a connected Slack connector appears for routine attachment and its MCP tools do not require another authentication step.

由索引模型根据 Issue 内容生成。