[BUG] Cloud Routine cannot access connected MCP connectors (Slack, Microsoft 365, Atlassian, Coralogix) — connector registry errors, PushNotification tool disabled

**Preflight Checklist**
- [x] I have searched existing issues and this hasn''t been reported yet (closely related to #35899, #43397, #45306, #54370, #63233 — filing separately since none exactly match this combination of symptoms)
- [x] This is a single bug report
- [x] I am using the latest version of Claude Code

**What's Wrong?**

I created a Cloud Routine ("Last 24h Brief") scheduled to run daily at 8:30 AM CEST, with Atlassian, Coralogix, Microsoft 365, and Slack connectors attached and "Runs with" showing all as enabled. All four connectors show as connected/authenticated at the account level and work correctly in normal interactive chat sessions in the same account.

When the routine runs (both on schedule and via manual "Run now"), the session cannot see or call any of the attached MCP connector tools. It falls back to only generic tools (Bash, git, file editing, web search, task tracking). Attempts to look up the connector registry from inside the routine session also fail.

**Environment Info**
- Platform: Claude (claude.ai), Cloud Routine
- Trigger type: Scheduled (daily 8:30 AM CEST) + Manual "Run now"
- Connectors affected: Slack, Microsoft 365, Atlassian, Coralogix (all attached, none reachable)
- Connectors confirmed working: Yes — all work immediately in interactive chat in the same account
- Additional tool affected: PushNotification — explicitly reported as disabled for this session type ("in subagents as well as here"), blocking the routine's Slack DM delivery step even as a fallback

**Steps to Reproduce**
1. Connect Slack, Microsoft 365, Atlassian, and Coralogix connectors at the account level; confirm each works in interactive chat.
2. Create a Cloud Routine with instructions that call these connectors as part of the task, with all four connectors attached and "Always allow"/enabled in the routine config.
3. Trigger the routine via "Run now" (also reproduces on the scheduled 8:30 AM daily trigger).
4. Observe the run transcript.

**Actual Behavior / Error Messages**
- Repeated "Failed to check connectors" errors when the session attempts to enumerate available MCP tools.
- Tool search for Slack tools returns "No matching deferred tools found."
- Session self-diagnosis: "None of the connectors this routine needs (Slack, Microsoft 365, Atlassian, Coralogix) are available in this session — only generic coding tools (Bash, git, web search) are present, and the connector registry lookup is currently erroring rather than confirming they're just disabled."
- Attempting to look up Slack in the connector directory from inside the session also fails: "Failed to search connector directory... The connector registry is erroring right now."
- Explicit tool error: "No such tool available: PushNotification. PushNotification is disabled for this session, in subagents as well as here."
- Despite all of the above, the routine run history in the UI marked both runs as "Completed"/succeeded (2 of 2 succeeded), even though no data was gathered and no notification/message was ever delivered — i.e. run status does not reflect task success.

**What Should Happen**
- Connectors attached to a Cloud Routine and shown as enabled in "Runs with" should be loaded into the routine's execution session at start, matching interactive chat behavior.
- If a connector genuinely cannot be reached for infra reasons, the run should be marked failed/degraded rather than "succeeded," so users aren't misled by the run history.
- If PushNotification (or any delivery mechanism, e.g. sending a Slack message) is intentionally disabled for autonomous Routine sessions, this should be documented and surfaced clearly in the routine creation UI, not discovered only via a runtime tool error.

**Related Issues**
- #35899 — Scheduled tasks cannot access MCP connectors until a user message warms the session
- #43397 — Cloud scheduled tasks cannot access MCP connectors — tools not loaded into session
- #45306 — Scheduled task MCP connector tools unavailable in execution environment
- #54370 — Schedule skill / RemoteTrigger API doesn't see MCP connectors connected on Team workspace
- #63233 — Custom MCP connectors not attachable to scheduled routines

This report additionally surfaces the misleading 'succeeded' run status and the PushNotification-disabled behavior, which I didn't see explicitly documented in the above.

Start by reproducing the issue with a Cloud Routine using the four listed connectors, checking both manual and scheduled runs and their transcripts. Trace the connector registry and PushNotification errors, then verify that attached tools load, delivery works or is clearly surfaced as unavailable, and unsuccessful runs are not marked succeeded.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.