Track full chat lifecycle and token usage in PostHog #102

Outcome

The /chat surface reports every meaningful step of a conversation through PostHog, including assistant responses, token consumption, model/provider selection, queued messages, and failures.

Current behavior

lib/openagents_web/live/chat_live.ex already emits two events:

• chat_message_sent when a user message starts a turn.
• chat_turn_completed when a turn finishes.

These do not include the assistant message, token counts, model or provider, message queuing, streaming progress, or non-terminal errors.

Work

Audit lib/openagents_web/live/chat_live.ex and lib/openagents/chat/open_router.ex and emit the missing server-side PostHog events through OpenAgents.Analytics.capture/3:

• chat_message_received — the assistant message was streamed or returned to the user.
• chat_tokens_used — a turn consumed tokens; include input_tokens, output_tokens, model, provider, conversation_id, and turn_id.
• chat_message_queued — a user message was queued while another turn was active.
• chat_turn_failed — a turn ended in an error or non-completed status, with reason.
• chat_stream_chunk — one assistant stream chunk arrived (rate-limited to avoid event spam, e.g. one event per second or per n chunks).
• chat_tool_called — the assistant invoked a tool, with tool_name and turn_id.
• chat_voice_started and chat_voice_ended — a voice session began or completed, with duration_ms.

OpenRouter token capture

Read lib/openagents/chat/open_router.ex and lib/openagents/chat/open_router/responses_stream_decoder.ex. When OpenRouter returns usage in a response or stream, capture chat_tokens_used once per turn, not per chunk. Do not duplicate counts across fallback paths.

Analytics queries

Update lib/openagents/posthog.ex so the operator analytics page shows:

• total chat_tokens_used per model and provider in the last day.
• total chat_message_received count.
• chat_turn_failed rate.

Acceptance criteria

• Every user message and assistant response is captured.
• Token counts match the usage returned by OpenRouter for each turn.
• No token or credential values are captured as properties.
• The operator analytics page renders the new metrics.
• mix precommit passes.

Dependencies

None.