[Improve] Offer bounded monitoring for ongoing processes

[roomote-roomote]

​Opened on behalf of @daniel-lxs. Follow up by mentioning @roomote-roomote, in the web UI, or in Slack.

Related issue

Requested in the linked task discussion; no linked issue. Inspected #2268, which remains open and proposes specialized required-check notifications; this change neither imports nor depends on that policy.

Why this PR exists

• A maintainer explicitly invited this PR in the linked issue or discussion
• I am a maintainer / this is internal Roomote work

Useful verification can happen after the current turn. Fast should offer that follow-up when it can resolve a concrete outstanding outcome, without turning every closeout into a monitoring pitch.

What changed

• Add three generic Fast prompt rules for bounded ongoing-process follow-up, rather than modifying individual workflows.
• Gate offers on a concrete unresolved outcome and actual verification capability. Ask one specific consent question with timing and a stop bound; never imply deployment or completion without evidence.
• Require acceptance before scheduling an offer while preserving direct scheduling for explicit monitoring requests. Revalidate capability, reuse equivalent wakeups, keep monitoring quiet and finite, and avoid duplicate notifications or repeated offers.
• Add three focused prompt-contract tests. No scheduling infrastructure or notification handlers changed.

How it was tested

• 88 tests passed: Fast prompt and wakeup args, parser and schedule suites via package-scoped Vitest.
• pnpm --filter @roomote/cloud-agents check-types and git diff --check passed.
• Normal pre-commit formatting and pre-push oxlint, residual lint, fast typechecks and Knip passed. Knip emitted one non-failing existing configuration hint.
• Browser proof is not applicable to this prompt-generation change. No live-model behavioral evaluation or real monitoring schedules were run; contract tests verify prompt content, not model compliance. Full root test suite and root pnpm lint/pnpm check-types were not run.

Checklist

• The PR title follows the repo convention: [Fix], [Feat], [Improve], [Refactor], [Docs], or [Chore] followed by a user-facing description
• This PR is small and scoped to one change
• pnpm lint and pnpm check-types pass locally
• I added tests or included a clear manual validation note above
• I removed secrets, tokens, private keys, and customer data from code, logs, and screenshots
• If this change should appear in the changelog, I ran pnpm changeset

[roomote-community]

1 issue outstanding. See task

• packages/cloud-agents/src/server/fast-agent/fast-agent-prompt.ts:342 The bounded-monitoring rule conflicts with the wakeup tool guidance that permits unbounded monitors.

_{Reviewed caa5a80}

[roomote-community]

This requires every monitoring schedule to be finite, but MANAGE_WAKEUPS_TOOL_DESCRIPTION still tells the model that monitors run until cancellation/resolution and presents unbounded every 10m as a normal choice. The scheduler also permits those schedules, so the conflicting tool guidance can still create an indefinitely running monitor. Align the wakeup guidance (or enforce a bound) so the new bounded-follow-up contract is reliable.