Claude Code CLI sessions don't expose claude.ai connectors (mcp__claude_ai_* tools never appear, even after full restart)

Summary

A claude.ai connector (GitHub Integration) shows as connected at the account level (Settings > Connectors > status ✓, type Web) but never appears as a callable tool (mcp__claude_ai_*-prefixed) inside a Claude Code CLI session, regardless of session freshness.

Steps to reproduce

1. Connect a connector (e.g. GitHub Integration) via claude.ai Settings > Connectors — confirm status shows connected.
2. In Claude Code CLI, ask the assistant to check for mcp__claude_ai_*-prefixed tools (or search for them via the tool-search mechanism).
3. Observe: no such tools are found.
4. Attempt each of the following resets, in order, verifying each completed before trying the next:

• /clear inside the running session
• /exit the process, then relaunch claude fresh in the same terminal
• Fully quit the terminal application (not just the tab/window), reopen, relaunch claude
• claude --version / claude update to rule out a version gate

1. Observe: connector tools still do not appear after any of the above.

Expected behavior

Either:

• Claude Code CLI sessions should be able to attach and use claude.ai connectors (with some documented mechanism for doing so — equivalent to the per-conversation connector toggle in the claude.ai web chat composer), or
• If claude.ai connectors are intentionally out of scope for Claude Code CLI sessions, this should be clearly documented, and any assistant-generated guidance (including the assistant's own in-session suggestions) should not imply otherwise.

Actual behavior

No connector tools ever appear, with no error message, no documentation found explaining the limitation, and no in-product signal distinguishing "not yet connected" from "not supported in this surface."

Compounding issue — bad assistant guidance

When troubleshooting this live, the assistant (running in Claude Code) incorrectly told me to move the task to claude.ai's standalone web chat interface, describing an "Artifact tool + mcp capability + window.claude.mcp.watchTool" workflow as if it were available there. It is not — that tooling (an Artifact publish tool with a documented mcp capability contract) belongs to the Claude Code product surface, not to plain claude.ai chat. Claude.ai chat has its own separate, unrelated artifact system with no equivalent. This sent me to try to execute a workflow with a completely different Claude instance that had none of the required capabilities, cost significant time, and caused real frustration before the mismatch was caught.

Environment

• Claude Code CLI, macOS (Darwin 25.5.0)
• Model: Claude Sonnet 5
• Connector: GitHub Integration (claude.ai Settings > Connectors), status: connected

Ask

1. Clarify (in-product and/or in docs) whether claude.ai connectors are expected to work inside Claude Code CLI sessions at all.
2. If yes: document the actual steps to attach one to a session, since none of /clear, process restart, full terminal restart, or CLI update surfaced it.
3. If no: ensure the assistant doesn't generate guidance implying it's possible, and doesn't route users to a different product surface based on an incorrect assumption about that surface's capabilities.