Scheduled/background sessions never register a connected connector's tools — enabledInChat:false, and the session's connector panel has no per-chat control

### What happened?

A custom connector added org-wide on a Team plan works in every interactive surface and
loads no tools at all in any unattended one.

In a Cowork/claude.ai scheduled task, the run reports the connector as authenticated at org
level with none of its tools loaded, then tells the user to enable it in "this chat's
connector settings". There is no such setting. The scheduled session's own connector panel
gives each connector a Connect or Reconnect button and nothing else, so nobody can carry out
the fix the run recommends.

Same connector, same account, same day: full `initialize` and `tools/list`, every tool
callable, in claude.ai chat and in Claude Code.

`enabledInChat` looks like a read-only per-session field. The `ListConnectors` tool
description instructs the model to advise enabling the connector in this chat's settings,
which makes sense in a chat and not in a scheduled run, so this bug keeps getting reported
as a user configuration mistake that the user has no way to correct.

### What did you expect to happen?

A connector that is connected at org level and attached to a scheduled task or routine should
have its tools registered in the session the trigger spawns, without an interactive message
first. If that cannot happen, the run should fail with the real reason instead of pointing at
a setting no surface exposes.

### Steps to reproduce

1. Add a remote MCP server as a custom connector. Team plan, added org-wide by an Owner,
each member connects individually over OAuth (DCR).
2. Confirm it works in claude.ai chat: tools are listed, tool calls succeed.
3. Create a Cowork/claude.ai scheduled task whose prompt needs one of its tools. Fire it.
4. The run reports the connector connected at org level with `enabledInChat: false`, has no
`mcp__*` tools in the session, and never attempts a call.
5. The routine/RemoteTrigger path fails the same way with `mcp_connections` populated.

### Area

Tool Discovery / Invocation

### MCP Server (if applicable)

Self-hosted governed MCP proxy, added as a custom org connector (name and host redacted).

### Error messages or logs

`ListConnectors` inside a cloud routine run (2026-08-26, trigger
`trig_01Py1yc1VMwNRyHAwHbLsAf3`), connector name redacted:

{"name":"[our gateway]",
"directoryUuid":"ccd70119-698c-4666-b752-119bc57605e6",
"installState":"connected","connected":true,
"isAuthless":false,"enabledInChat":false}

`ToolSearch` for that connector's tools returns "No matching deferred tools found". This is
not an auth failure: `connected` is true, and the same grant works interactively.

Scheduled task run, 2026-09-07, verbatim with the connector name redacted:

the [our gateway] connector is toggled off for this chat. It's connected and
authenticated at org level (installState: connected), but enabledInChat is false, so
none of its tools are loaded and no metrics query could be made. Fix: enable the
[our gateway] connector in this chat's connector settings, then re-run the task.

### Additional context

Both unattended surfaces fail identically for us: Cowork scheduled task on 2026-09-07, and
routine/RemoteTrigger on 2026-08-26 and again on 2026-08-14. That looks like one gap in how
scheduled and background sessions receive their tools rather than two separate bugs. Spawning
a subagent does not help. Neither does removing and re-adding the connector in the routine's
Connectors tab.

Custom connectors are not the limiting factor. #545 in this repo is the mirror image: a
custom connector whose tools bind correctly in Routines while interactive chat never sends
`initialize`. The scheduled path can bind a custom connector.

The closest existing reports all live in anthropics/claude-code, and the two nearest were
closed by the inactivity bot while still reproducing: anthropics/claude-code#73845 (closed
2026-09-06, retested on 2.1.220 eight weeks after filing) and anthropics/claude-code#79319
(closed 2026-09-05). Still open there: anthropics/claude-code#90972 (Cowork scheduled task
attaches nothing), anthropics/claude-code#91819, anthropics/claude-code#88594,
anthropics/claude-code#92006. The routines documentation says all connected connectors are
included by default and callable without approval prompts, and anthropics/claude-code#52586
was closed as shipped on 2026-08-17.

What this costs us: our gateway is the only sanctioned route to Jira, Confluence and Datadog
for our users, so no scheduled task any of them writes can reach those systems, and
connecting each vendor's own connector instead is not an option open to us.