feat: deliver Lavish board feedback via a re-armed watcher check

[psacc]

Summary

Fixes the intermittent failure where Lavish board feedback sent from the browser never reaches firstmate through the armed lavish-axi poll listener.

Root cause (reproduced end-to-end): lavish-axi poll is a single-shot long-poll that returns and exits on the first wake event, and browser-generated layout_warnings share that wake channel with real user sends. So a warnings event returns an armed poll with empty prompts, and a human send that then lands with no poll armed waits in the queue until the next arm.

Fix

Model the poll as a per-board watcher check instead of a fragile long-lived poll process:

• bin/fm-lavish-check.sh generates and registers (via fm-check-register.sh) a state/<task-id>.check.sh that, each watcher sweep, runs a short-timeout lavish-axi poll (drain-on-arm delivers any queued prompts) and prints a wake line only when real user prompts arrived. Warnings-only, waiting, and ended-without-prompts returns stay silent, and the watcher re-arming every sweep makes delivery reap-proof.
• Two operational rules added to the bearings skill, which owns Lavish board usage: never treat an empty-prompts return as feedback, and never arm two polls on one board file.
• Colocated tests in tests/fm-lavish-check.test.sh.

The classifier parses lavish-axi poll's human-readable text digest (the CLI has no --json flag in 0.1.42): a non-empty send renders a prompts[N]{...}: header while an empty one renders prompts: [], and the header match is line-anchored.

Validation

Validated locally by captain decision. The no-mistakes pipeline was intentionally bypassed to avoid reconfiguring the shared firstmate gate while the upstream k2 (kunchenguid#672) and herdr (kunchenguid#648) lanes had live runs on it.

• 11 colocated tests pass (tests/fm-lavish-check.test.sh).
• shellcheck clean at the pinned 0.11.0 (per bin/fm-lint.sh).
• End-to-end against the live Lavish server: warnings-only stays silent, real prompts wake with a count, and drain-on-arm delivers then clears.

Out of scope

A separate whole-file lost-update race inside the third-party lavish-axi state store was found during the investigation; an upstream bug report is drafted but not filed.