Show LLM provenance in PR-review and Slack automation output

Problem or Use Case

The GitHub PR-reviewer and Slack channel-monitor automations publish LLM-dependent judgments without identifying the LLM profile and model that generated them. The original report is OpenHands/automation#430, but these output implementations are owned by this repository.

Desired Behavior

Published PR reviews and Slack automation responses should include the LLM profile and concrete model used for the underlying conversation, using the same concise wording.

Acceptance Criteria

• GitHub PR-review automation output displays its LLM profile and model.
• Slack channel-monitor output displays its LLM profile and model.
• Both automations use consistent, concise wording.
• The displayed profile and model match the concrete agent settings used by the spawned conversation.

Additional Context

This same-repository tracking issue allows the Extensions PR readiness check to validate ownership and readiness while retaining the original cross-repository report as context.

This issue was created by an AI agent (OpenHands) on behalf of the user.

Start by locating the GitHub PR-review and Slack channel-monitor automation implementations and tracing how each spawned conversation receives its agent settings. Compare both output paths and verify how the concrete LLM profile and model are available. Done means both outputs show the matching profile and model with consistent concise wording, with the relevant checks passing.