Conversations: AI chat in the support widget

Is your feature request related to a problem?

When no support agent is online, or before one picks up a conversation, customers in the Conversations support widget wait for a human reply even for questions that could be answered instantly from docs or previous tickets.

Describe the solution you'd like

An AI chat option in the Conversations support widget: an assistant that answers customers directly in the widget, grounded in the team's documentation and knowledge, and hands off to a human agent when it can't help or when the customer asks for a person.

This pairs well with a working-hours away message (#70074): outside working hours the AI can keep helping while the widget sets expectations about when humans reply.

Describe alternatives you've considered

Agent-side AI assistance (suggested replies for humans) improves reply quality but does not reduce time to first answer when nobody is online.

Additional context

• Requested by a customer through a support ticket, together with the working-hours away message in #70074.
• The backend already has a grounded support reply pipeline (see run_support_reply in products/conversations/README.md) that could power customer-facing answers in the widget.

Start with products/conversations/README.md and the run_support_reply pipeline described there. Trace how it could serve answers in the Conversations support widget, including grounding in documentation and previous tickets. Done means customers receive AI replies when appropriate, can request a human, and are handed off when the assistant cannot help.