[Docs] Advisor tool is not inherited by background subagents, contradicting the advisor docs

Observation

The advisor docs (https://code.claude.com/docs/en/advisor) state:

"Subagents inherit the configured advisor and apply the same pairing check against their own model."

In practice (Claude Code v2.1.206, Windows 11, main model Fable 5, advisorModel set to fable via /advisor), inheritance only works for synchronous subagents:

• A subagent launched with run_in_background: false (model: sonnet) had the advisor tool and called it successfully (the advisor confirmed it received the subagent transcript).
• All subagents launched in the background (default since v2.1.198; models opus and sonnet, subagent_type: general-purpose) consistently reported the advisor tool as unavailable — observed across ~8 independent runs in one session, zero exceptions.

Repro

# WORKS: foreground subagent gets the advisor tool
Agent(..., run_in_background: false)

# FAILS: background subagent has no advisor tool
Agent(..., run_in_background: true)   # or omitted (background is the default)

Question / Request

Is this intentional (similar to MCP tools being unavailable in background subagents, #13254 — closed as not planned)?

If intentional, please document it on the advisor page, e.g.:

1. "The advisor is not inherited by background subagents."
2. "Set run_in_background: false if advisor consultation is required in a subagent."

If unintentional, enabling advisor inheritance for background subagents would be valuable — background is the default since v2.1.198, so in practice most subagents never get the advisor despite the documented inheritance.

Environment

• Claude Code v2.1.206, Windows 11 (native, PowerShell)
• Main model: Fable 5, advisor: Fable 5 (pairing valid per docs)
• Subscription auth (claude.ai), advisor works normally in the main loop

Cross-ref: #13254 (MCP tools unavailable in background subagents)